Why do succubi and incubi hunt and seduce humans, lore wise? 

This is dependent on which lore you want to follow, demonic and devilish succubi (which are different) do so for different reasons. Demonic succubi/incubi do so specifically to create affairs with mortals and ruins mortal relationships and cause chaos. Devilish incubi and succubi on the other hand do so as more  of a means of offering power or pleasure, thereby providing more of a societal corruption in the long run, as well as getting a soul out of it.

Neutrally it is because fiends cannot conceive on their own, in contemporary literature one thing that a succubus would do is seduce a man to gather his seed, then transform into an incubus (through shapeshanging) and deliver that seed to a woman by seducing them. The result would most often be a fiendish child, in D&D it would be like a cambion, tiefling, alufiend, or even a rare pureblood succubi or incubus

Per the entry Succubus seduction to cause the mortal to perform evil acts, so their soul descends into the lower planes.

MrPCOX above gives some excellent examples.  In the current 5e, since they are no longer strictly Demon/Tanar'ri as they were in prior editions, they can serve many different type of masters.  So, one serving Graz'tz could be about hedonism at any cost, whereas one bound to Glaysa would using seduction to increase her crime network on the material plane.

So the question might be better stated as "Who does the succubus serve, and how can they using seduction or manipulation to achieve their master's desires."

Quote from MrPC0X >>

Neutrally it is because fiends cannot conceive on their own, in contemporary literature one thing that a succubus would do is seduce a man to gather his seed, then transform into an incubus (through shapeshanging) and deliver that seed to a woman by seducing them. The result would most often be a fiendish child, in D&D it would be like a cambion, tiefling, alufiend, or even a rare pureblood succubi or incubus

 
In D&D 5th Edition incubi and succubi can procreate with humans or each other without needing to shapeshift into different genders. Offspring between incubi and succubi produces full incubi/succubi. Offspring between incubi/succubi and humans produces a cambion. Neither can make a tiefling - which can only begotten by a Tiefling and human. The tiefling line are a result of a curse that affected the blood of a human using the blood of a high-level fiend (most commonly Asmodeus). The race was not started through procreation - it's a curse, but it can be passed down as lineage. And finally, there is no such creature as an Alufiend.

D&D 5th Edition is usually very different from real worth mythology. It's often best to not confuse the two.

Quote from Cyb3rM1nd >>

Quote from MrPC0X >>

Neutrally it is because fiends cannot conceive on their own, in contemporary literature one thing that a succubus would do is seduce a man to gather his seed, then transform into an incubus (through shapeshanging) and deliver that seed to a woman by seducing them. The result would most often be a fiendish child, in D&D it would be like a cambion, tiefling, alufiend, or even a rare pureblood succubi or incubus

 
In D&D 5th Edition incubi and succubi can procreate with humans or each other without needing to shapeshift into different genders. Offspring between incubi and succubi produces full incubi/succubi. Offspring between incubi/succubi and humans produces a cambion. Neither can make a tiefling - which can only begotten by a Tiefling and human. The tiefling line are a result of a curse that affected the blood of a human using the blood of a high-level fiend (most commonly Asmodeus). The race was not started through procreation - it's a curse, but it can be passed down as lineage. And finally, there is no such creature as an Alufiend.

D&D 5th Edition is usually very different from real worth mythology. It's often best to not confuse the two.

You would do well to remember that this game draws from many resources including older generations. The concept of a Tiefling being brought upon by a curse is largely a 4th edition idea, while tielfings have been a result of demonic (or equivalent) lineage for quite some time, being a rough equivalent to aasimar in older editions. The Alufiend, which you deign to say does not exist, actually comes (mechanically) from 3es Monster Manual 2 wherein it is specifically described as the female offspring of a succubus and a male human. A Cambion would be the male equivalent to an alufiend given the system's history.

In addition it has LONG been established that fiends and celestials (azata, archons, emyreals, etc.) cannot procreate of their own accord, that is a fiend cannot breed with another fiend, and an angels cannot breed with another angel, each higher race in such a position has different means of procreation (such as through petitioners). Succubi are no exception to this. Without a mortal they cannot procreate easily, that is to say unless they expend a significant effort to raise a lost soul larva (or the equivalent found on their home lower plane) into a suitably ranked succubi/incubi.

I'm not interested in previous editions. This is 5th edition, my answer pertains to 5th edition only.

I suppose that's a shame really, but that is your choice then. The answers I gave are not any less factual or correct. I don't see 5th edition as any more than a new mechanics system that has been refurbished from other systems like 4e and 3.5.  It is not entirely self contained and it's lore and the lore it was founded on spans a period of almost 50 years.

Although, I suppose it is here we will agree to disagree.

Quote from MrPC0X >>

I suppose that's a shame really, but that is your choice then. The answers I gave are not any less factual or correct. I don't see 5th edition as any more than a new mechanics system that has been refurbished from other systems like 4e and 3.5.  It is not entirely self contained and it's lore and the lore it was founded on spans a period of almost 50 years.

Although, I suppose it is here we will agree to disagree.

There is a lot of story and lore from prior editions which many of us find cool.    But even the various settings have different stories concerning their monsters and lore.  For example, Drow are very different in nature and lore between Eberron and Faerun.  The same applies to fiends in those worlds (the roles of rakshasa, the lack of a Blood War, etc). 

So, at the very end of the day, its not what the books say, but the DM chooses to incorporate.  By 5e rules, there is no Queen of the Succubi, Malcanthet.  Lots of lore on her, and many other demon princess.  But if a DM wants her to be relevant, she is.

Per Xanathar's Guide to Everything, a human/devil pairing can produce a tiefling offspring.  And human(oid)/fiend pairings of other types are not explicitly listed as impossible.

Also, devils were the only type of fiend that was ever explicitly stated to be unable to procreate (with the exception of erinyes, who were able to due to being fallen angels).  Demons, yugoloths, and celestials did not have any such restrictions, if they have them now it's a recent change.

I agree, I merely make the point that 5e does not contain all the answers. A simple change of mechanical system does not erase the value of the previous one.

Using Malcanthet as an example. Perhaps she has been omitted because of her lack of immediate relevancy. A good example is the importance of Demon Lord Fraz-Urb'luu who remained entirely absent from 4th edition (as opposed to Orcus or Lolth) despite his level of importance lore wise and combat wise in previous generations of the game, only for him to return here in 5th edition. I would never have known about him had I not dabbled in 3.5 and 5e.

Like you said, ultimately it is up to the DM what they wish to incorporate, especially if they are running a homebrew campaign or setting. But they have far more than 1 book in 1 system or setting to draw on if they want answers or ideas; just like with the drow you mentioned.

I mean, for a bit of an ironic laugh, I'm still waiting for any mention of Azuvidexus the demonic T-rex.

Quote from 6thLyranGuard >>

Also, devils were the only type of fiend that was ever explicitly stated to be unable to procreate (with the exception of erinyes, who were able to due to being fallen angels).  Demons, yugoloths, and celestials did not have any such restrictions, if they have them now it's a recent change.

I'll have to eat some of my words then. In retrospect I wouldn't put it past demons to be able to do that but as for angels (whom I was fairly certain could only be created by petitioner soul) I was aware they could procreate with other creatures (though a reason for doing so eludes me) but I couldn't find any true evidence that they did so among themselves.

It's not an unreasonable assumption, especially given how they've been changed in 4th and 5th edition to be more alien and removed from mortals, but I'm not aware of any source that explicitly says that they can't.  I do know that there are individual celestials that were never petitioners.

Quote from MrPC0X >>

Quote from 6thLyranGuard >>

Also, devils were the only type of fiend that was ever explicitly stated to be unable to procreate (with the exception of erinyes, who were able to due to being fallen angels).  Demons, yugoloths, and celestials did not have any such restrictions, if they have them now it's a recent change.

 

I'll have to eat some of my words then. In retrospect I wouldn't put it past demons to be able to do that but as for angels (whom I was fairly certain could only be created by petitioner soul) I was aware they could procreate with other creatures (though a reason for doing so eludes me) but I couldn't find any true evidence that they did so among themselves.

Well, in forgotten realms, demons could add to their numbers by stealing souls from the Wall of the Faithless in the fugue.  Supposedly they couldn't reproduce to create more fiends directly, but then you have Draegloths (requiring a ritual, a drow female, and a Glabrezu.  Succubi and by extension Lilitus and radiant sister could, as could erinyes on the devil side.

Yugoloths, could reproduce normally...dont want to think about that.  And celestials can, but don't generally with the exception of creating aasimar bloodlines.  Why is a question?  Love or fate or necessity?

Its never been that consistent even within an edition...cambions, alufiends...some one is doing all the begatting.  

In my world, Succubi and Inccubi are the same thing. They can assume either gender, but both are sterile. So in order to reproduce they must assume their Succubus form, seduce a male to get their... “genetic material.” Then while it is inside them they mutate it so that when they transform into Inccubus form and seduce a female, they can then impregnate them with it.