Biking while too drunk to drive is probably still a bad idea. Not as bad as driving a car, but you can still cause a serious accident on a bike, especially on roads in the US where there aren't even bike lanes in most places.

You can still get a DUI riding a bicycle, if you can believe that. It's fucking stupid as shit, but I know someone whose life was turned upside down because he chose to ride his bike to a bar, thinking he was being responsible.

There is a bar not far from me that has an old public transport bus and a passenger van they use to take people home. I think it's a cool idea because as you say, there isnt a public option.

And of course biking and walking isn't an option, because if you walk or bike home you'll get a public intox rap.

Also being drunk in public is a crime in many states, so other than ride sharing you're mostly SOL.

Okay I know this is crazy, but if you just take the drunk person into account and the the only options are walk, bike, or drive. The safest thing for them to do is drive home drunk. Mind you this study was only done with data from America so that may be different in places with different urban planning. And yes that is terrible