Public transit doesn't run enough. In Japan, which has one of the most functional train systems in existence, staying out late (and not even very late!) means paying for a hotel room or post-drinking room (they serve you snacks and wash your clothes, etc).
This is in Tokyo.
Public transportation can't replace private vehicles. It can help. It can be useful. It can't replace them. It's like trying to replace traditional powerplants with wind - it doesn't work.
Do you think this problem really matters? There is a whole industry around capsule hotels anyway, I've spent a bit of time in Tokyo and no one is highly inconvenienced from staying out till 3am having a wild time on the town.
If you do get stuck, you do what everyone else does, get one of the probably millions of taxis to drive you home.
Let's face it the taxi driver will at least help you get out of the car :)
Lastly, many people who stay out that late are hammered and probably going to spew in the car, that won't be fun.
This is in Tokyo.
Public transportation can't replace private vehicles. It can help. It can be useful. It can't replace them. It's like trying to replace traditional powerplants with wind - it doesn't work.