Likewise "operational separation" of different lines is key to reliability, both to ensure incidents on one line don't affect service on another, and because points are subject to a lot more wear and tear than plain track (see the current disruption to south London rail services, caused by a cracked crossover at Lewisham). Going forward TfL is trying to move towards a network of simple, self-contained end-to-end lines, e.g. by separating the Northern line into two independent lines rather than one line with five branches.
The kind of thing you're describing is in operation elsewhere in London where the capacity requirements make it more appropriate: http://en.wikipedia.org/wiki/ULTra_(rapid_transit)
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 ?
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.
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?
Because subway lines are fixed, have little branching and your carriage can't magically jump from one line to the other? Having independent carriages would mostly be messier, for no advantage.
The system you purpose would not be traffic-immune. A large train full of people is incredibly efficient. You are describing autonomous cars, which will be great and given the the size and number of roads they don't need to match the efficiency or rail lines.
I understand in 1798 why they went with one locomotive and lots of carriages. The engine is too expensive. One driver per carriage is not feasible. Great. All of those are eliminated. Electric motors are cheaper than "real" breaks, so every 2 wheels have an electric motor anyway. And if you have to have them, people power the train using the lots of small motors, because that means no big engine in the first carriage.
But given that you need those things, why can't we just have every carriage be it's own "train" ? Why can't every carriage just have the destination that would be most convenient at that moment in time ?
Why can't London subway be a traffic-immune taxi service ? Now THAT, I want.