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