Not an issue of spaces per se but with >1000 rooms/DMs, the Element Desktop UI can become very unresponsive, to the point of being barely usable, and sometimes freezes completely requiring killing the process. I haven't pinpointed the exact condition(s) that makes it freeze up/get very sluggish but even on good days it takes >5s to expand the "People" list.

This is on a modern desktop CPU with plenty of memory headroom. It never happened so far on a profile with less chats.