I have no idea how neocities is implemented, but my first thought as far as implementing something like that wouldn't be to give users actual filesystem access, but rather to put everything in an object store. Typically that'd be flat until you bolt on something to simulate a hierarchy.
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.