Maybe they should have scheduled maintenance closures that reoccur over the same parts of the day every day. Say, 1-5am?. So, it would be a 20hr/day instead of 24hr/day subway, but would be dependable during those 20 hrs.
It got a bit less overwhelming when they started running the night buses from all over central London rather than just from Trafalgar Square. It's changed again recently now that some underground lines are 24 hour.
assuming I can get someone to actually take me across the bridge
It is possible to stay at a private club until the train restarts around 5am. Alternates is Internet / Manga Cafes complete with shower rooms, coin operated clean underwear dispensers, and lounge chairs that lie almost flat. Also helpful is the convenience stores that sell dress shirts.
Obviously, some people work overnight shifts or have other critical needs for transport around the clock, so there needs to be a reasonable level of public transport services for that purpose. But if the problem is that people can't stay out late at bars, then... maybe they just shouldn't stay out late at bars if they don't have a way home?
I am deliberately ignoring the obvious issues with drink driving risks, flow-on effects of the "nighttime economy" and so on here. Also, I'm an introverted non-drinker who doesn't understand why people are out drinking at 2am when they could be sleeping at 2am... So more practically, yes, you need decent coverage of night-time substitute bus routes.