Android 4.0 would be especially good for this, since it looks better on bigger screens, so once you hook the phone to the bigger screen, it could just show you the same OS, except in "tablet mode" (like the the apps).
Yes, I don't think we need a huge jump in OS capability for something like that. For one, fullscreen apps are pretty common even on desktop machines. Most Windows users I know run like that pretty much all the time, and OS X Lion seems to go that way, too.
Apps that need finer grained control often are perfectly fine doing it themselves, e.g. a terminal application with split screes – or simply using screen/tmux.
If the OS would support some primitive tiling (mostly to have two apps side by side on a full HD class display), I'd say that 95% of the people would be happy 95% of the time.
The biggest issue I'd see is app diversity. Some apps might be willing to target all of the devices, some won't. But no matter how perfect your app is on small screens, if it will just scale badly to larger ones, people will complain. There would probably be a need for some finer-grained selection in the app launcher, clearly labeling what would be fine to use now and what not.
