It is a bit of a laugh to drink your character into oblivion and watch them stumble around for a while, but what is the actual point of being able to do so in a game? Games like Red Dead Redemption and GTA have the ability to drink, but beyond making the screen blurry, there is nothing to it.
Players might use it once, but for something that took developers time to animate, develop assets and effects, it's useless. Maybe that development time wasn't vital, but it could have been put to better use and not simply made to create a passing annoyance if anything.
It is such a common feature that it is baffling how much it crops up. If its to do with immersion, then there is a small case to be made for it, but staggering out of a bar drunk of your head isn't exactly at the top of the list for immersive play.