Disclaimer: This isn't an excuse for drink-driving, you should think about this before you go out, but clearly there are a lot of people who either don't think about it or can't help themselves.
- Taking the bus which didn't run anytime after 10pm - Calling a friend which really only worked when you planned ahead - Calling the local taxi service which was limited and was pretty expensive unless you had a ton of people riding with you. They did "drunk bus" kind of rides mostly.
Planning transportation (DD, drunk bus, etc) was really the only way to get home unless you just walked everywhere. The fraternities and sororities ran DD systems for their members and friends which I admired but couldn't take advantage of. After Uber came out, use exploded and the DUIs started going down.
But if you are the kind of person the police takes care of on a bench multiple times then it's within their (or rather the relevant authority, not the police) power to consider a person "unfit" for having a drivers license. Won't happen to "normal" people, even if on a bike.
You're still posing a traffic hazard.
For starters, I can usually go most places by bike without doing it on the same roads as cars. (I know that's rarely the case in the US though). If that's not possible, and you are so drunk you can't ride a bike (I can certainly ride a bike safer than a car while drunk simply because the speed is much slower so the reaction times are longer) - then leave the bike too. Walk or get a cab.
Situational awareness is an entirely different story though. In the dead of night traffic is on easy mode, where you notice the indirect illumination of a car's headlights around two corners and hear them from a mile away. That's just not very challenging (and probably plays a large role in the seemingly universal pattern of more drunk driving in rural areas, unfortunately cars come with an incredible amount of risk compensation through speed). Broad daylight city cycling on the other hand I consider a bad idea even at BAC levels well within the legal limits for driving cars (speaking of Germany here, where in terms of fines, cycling is tolerated at twice the BAC level as driving, a reasonable compromise)
Road traffic relies on cooperation between the participants. If you can't pull your own weight (i.e. follow traffic laws, control your vehicle, etc), you don't belong on the road.
Also it's not about yourself. Sure, if you kill yourself in an accident on a bicycle you're less likely to injure somebody else but you're still inflicting all kinds of harm on others.