Then do what most modern systems are moving to anyway : eliminate the track. Work with just bog standard roads in the tunnels and eliminate the rails, built and maintained like any other road.

I feel all of those problems are solvable, and it would be a huge improvement. The fact that railways have multiple lines is at least half the reason I don't want to use them. Same with the tube.

Today, using the tube is torture. Constant interchanges, deep long extremely crowded hallways, and it's getting worse every year. Why can't that be fixed ?

There's nothing "bog standard" about underground roads of that length. Unsignalled vehicles would not be safe (IMO it would be reasonable to relax some safety constraints on the british railway to increase capacity - it would save more lives by taking people off the road - but that would be politically unacceptable; people respond irrationally to major disasters). Unguided vehicles wouldn't fit down the current tunnels. And vehicles with emissions would require much more ventilation than currently exists for the deep tunnels. So you'd need something like a guided trolleybusway with custom vehicles, you'd still need some equivalent of pointwork for the electrical supply, and the vehicles probably couldn't be as heavy or as fast as rail ones.

I don't think I'm advocating unsignalled. Just put the signalling into a distributed system into the trains themselves. Since those vehicles can actually see what's in front of them, that should be a lot safer, since signalling systems are effectively blind (that's where the disasters tend to happen. The central system wasn't aware of, say a broken connection that put a switchboard into an unexpected position).

I'm convinced this can be made safer than central signalling.

As for the vehicle sizes, I'm sure whatever size vehicle is necessary could simply be constructed, and the article on wikipedia for mentions that you could have battery-powered vehicles with rapid charging at stations, negating the cost of having and maintaining dynamic (moving ?) electricity connections throughout the tunnels.

Modern ERTMS involves the system knowing where all the vehicles are; a centralized system will be more efficient than a distributed one if all the information is available. I don't think that's a fair characterization of British train disasters; the only one I can think of that involved a signalling failure is the Clapham Junction crash, in which the wires were connected wrong - and connecting the wires wrong will break any system.

A vehicle the size of an 800-person tube train wouldn't be able to get round the tube corners without rails, and how could you negotiate a destination that made sense for that many people?