If you want a recent and feature complete server that performs better than the official one check out PaperMC. That's basically the de-facto standard for servers these days anyway.

It's better but still fairly resource-intensive. I'm wondering why it's so as the main work is being in the client, whereas the server concentrates on updating the structures close to the player - the rest of the universe is either generated or loaded on the fly. I'm fairly sure this could be optimized much more.

A video games server must compute a lot of things for each client otherwise it would be too easy to cheat.

It is easy to cheat on minecraft. It has a completely broken security model.

For a private server where access is whitelisted I'd sacrifice cheat protections for speed.

Granted, but should it matter on a private server run among friends who don't cheat anyway as they feel it would spoil the game?

If you'd like, try other Minecraft server software. I used Bukkit back then, and I saw people report on its better than vanilla performance.