Q: must a TimeMachine share be local?

My guess? Really hard problem.

But if you want this, go ask Apple directly.

Why hard? Because AFP and NFS and SMB add a layer of complexity and of potential instability into and added error-recovery within what is intended to be a reliable means to archive data?

You already have one network connection involved between the client and the server, and it's non-trivial to have entirely reliable disk access with a network between your TM server and your disk when you have a network involved. Not to mention that you've doubled your network traffic.

While there's local caches, those are typically managed under the control of the operating system and comparatively manageable.

Most (all?) remote services also cache data, so you're not really sure what's been written to disk unless you shut off that caching, and performance tanks, or unless you wing it and hope it all gets written; recovery from a failed cache is nasty, and Unix already has enough "fun" when the box "drops" before the I/O caches get written.

If you need this capability, then have a look around for end-to-end backup services; there are commercial packages which can stream data and manage connections out to a remote disk server or remote tape drive. But it might also be cheaper here to get yourself a bigger disk array, or a Mac with more expansion; a bigger RAID array or an upgrade to a server with FC and with a SAN storage controller or such.