Why don't gods take warlocks and what would it look like if they did?

I would say you can have a god as a patron, but why would they make a Pact with a mortal? I would mostly consider it a variant cleric or druid type, with the God being a patron type already published like the celestial (Good God), the Archfey (Trickster or Elven God), Fiend (Evil God) or such.

An alternative way to look at that scenario is that you as the warlock may be working directly for the god, but he uses an emissary in the form of an angel/demon or what have you to give you your guidance.  Though you maybe doing "Gods" work you may not directly interact with them except in special occasions, with them typically using an intermediary.

Quote from Conn_Eremon >>

It would look like a cleric, or a paladin or a druid. It's a matter of scale. A god's ability to grant power far exceeds that of a Warlock's patron, and is more interwoven in the world. A god's attention may be brought to bear on a singular individual, but that is not how their "pact" works. Rather that is more that their "pact" is freely given to any and all that embody the values and virtues (or lack thereof) of the god.

That said, looking for creative ways around this sort of thing is certainly possible. You could always use the Celestial Warlock mechanics while role-playing as a cleric or paladin for instance. I really like the idea of a Celestial Warlock being granted power specifically and directly by an emissary of his or her god. That'd work very well with an Aasimar, as their angelic guide and patron could be one and the same entity.

. . . To the character builder!

Ability scores: 12 15 11 10 17 12

 That is kind of what has happened in my game, one player is a bright lock, another is an aasimar bard.  Both of them have connections to the same powers though they do not know it.  A god was beseeched to save a child and sent an angelic messenger to protect said child from evil, something like Harry Potter at its root.  The Brightlock made a pact by repeating a ritual he heard (kenku) and is now in a pact with an angelic deity.  Both of them are being guided by the same higher power masquerading as something lesser (A god shows up in whatever form is appropriate).  so i had a two part version of what you are suggesting.

This recently came up in my campaign. One of my players met Bahamut in his wandering Gandalf form and they discussed the nature of gods (this player was from Athas cause planescape) Bahamut made clear that the character was too much of a free spirit not really wanting to be beholden to rules or a code to be one of his clerics (mainly because you tend to find in some expanded works the ideas gods have strictures and coodes that their priests have to follow), but the character does has the option to be granted some of bahamuts power without the stricture implementation via ceelestial warlock, mainly due to good roleplay and being a character that is a good and just person without needing to be told.

I mean if you really deconstruct it to its most fundamental levels, a cleric of a deity is an awful lot like a warlock just with a less personal and direct relationship between them.