There is at least one subclass that can use its weapon as a focus however they created the Ruby of the War Mage a common magic item that requires attunement : Etched with eldritch runes, this l-inch-diameter ruby allows you to use a simple or martial weapon as a spellcasting focus for your spells. For this property to work, you must attach the ruby to the weapon by pressing the ruby against it for at least 10 minutes. Thereafter, the ruby can't be removed unless you detach it as an action or the weapon is destroyed. Not even an antimagic field causes it to fall off. The ruby does fall off the weapon if your attunement to the ruby ends.
Based on this Item I would say you shouldn't be able to make your weapon a focus without the ruby.
That being said I have a Gloom Ranger/ Forge Cleric in AL that I used Blessing of the Forge to attach holy symbols to my Oath Bow, my +1 Long Bow, and my starting Long Bow. So far I haven't had anyone challenge it and it allows me to have a holy symbol in hand if I have my bow in hand. And I think it's fun to say that Guiding Bolt leaves the bow like an arrow but it does nothing mechanically.
I think that to see what might be possible with an arcane focus we just have to look at them as a group. If we look at the ring focus, it is equipped at all times and always on your hand. So there is no reason why this particular form of focus should have such an advantage over the others. (even though a crystal orb costs a fortune :D and does the same thing) Further more, we have spells that can be used along with a weapon, so there is no reason for a weapon to mess with the spell somehow, since other spells work fine with it. In 5e armor doesn't restrict casting as long as the caster is proficient with the type of armour. Any rules that made heavy armours interfere with magic (because metal, I hate it when I can't make my wizard staves out of metal) are not in 5e (which is why we have eldrich knight and war clerics)
So you have 1) spells that prove weapons are not a problem 2)armor is not a problem 3)an example of a focus that definitely supports this *4) if a staff can be a focus and a solid weapon at the same time (damn druids) who says a longsword (which has the same damage as shillelagg btw) couldn't be?
The addition of Ruby of the War Mage suggests that RAI is the weapons otherwise not be able to serve as an arcane focus. Even if you affix the crystal that can serve as an arcane focus to them.
If Xanathar's is to in play, and there for no Ruby of the War Mage, it seems to me reasonable that an arcane focus crystal could be affixed to a weapon and used for spell casting. The caster would only get the benefit of the crystal as a focus while they were holding the weapon. This could prove awkward in some social situations, and if the character lost the weapon they would lose the focus.
Using any old weapon as an arcane focus is not possible, unless you have the bardic ability.
A staff used as an arcane focus is specifically designed for use as such. You can't just grab any old quarterstaff and cast spells through it. The rules do not explicitly say either way if a staff designed for use as an arcane focus can also be used as a quarterstaff in combat. The Lord of the rings movies show a reasonable justification that it could.
Any material component or arcane focus requires a hand free to manipulate it during casting. With a holy symbol on a shield the shield can be manipulated along with the holy symbol. I would see this as the shield functioning as a holy symbol in this case.
So, ultimately DM's call as to whether or not to allow a crystal on a sword hilt to be used as an arcane focus. In general the rules seem to downplay the requirements of V, S, M spell components in favor of ease of play.
As for arcane focus vs component pouch, both can be taken away. A caster without either can still cast spells with a material component if they can access the appropriate component. Many common spell components should not be that hard to find, a pinch of sand, a tuft of wool, etc. Arcane foci and component pouches just mean you don't have th ebook keeping of which ones and how many you are carrying.