Seems like a smart way to do it, but that relies on having another always-on system standing as the server. OP's solution only requires the one device, the rPi unless something needs to be changed.

That's true. In theory you could use an extra Raspberry Pi itself as the netboot server. But since my home network already has a fileserver it was an easy choice.

If you run an open source router distro like OpenWRT or OPNSense, you can use it as the PXE Boot host. That's a device that needs to be running anyway.

I've seen a lot of people running their routers as a VM on something like Proxmox and that gives you even more flexibility but it does require a beefier server - one that could potentially replace all the RasPis, potentially making the PXE boot redundant. :D

Can you netboot from a desktop computer that's not always on? If the desktop is running when the pi is booting, does the pi then need the "server" (desktop pc) again until it needs to reboot?

No, because the root filesystem is mounted by NFS.