What you ask for is already possible for a few bucks a month with countless VPS hosts. This is free, remember?
Also, the OP isn't part of the NeoCities team. He's merely an advocate for it.
I've run forums even on rickety DIY PHP + Postgres that's held up very nicely to several hundred logins and even more sessions per day on very modest hardware (1.5Ghz Core 2 duo, 2Gb memory).
It doesn't take a boatload of resources for a simple login and static content if it's just static content. Sites can be separated (or "sharded" if you like that term) on Nginx with very little effort for static content.
E.G. https://gist.github.com/perusio/2154289
There are more elegant solutions for that which still don't require blob objects.
Then make a noexec chroot which has just a /home for them all.
I'm not sure how you'd translate a http request with an authenticated session into a handler running as a particular user, but I don't doubt that it is possible with some fork(), setuid() arrangement.
What would be wrong with giving people a chrooted slice of noexec filesystem with a usage quota set, that they could manipulate as they pleased?