Ults? Most are able to solo them with ease now (except Dark), so most of them aren't shared. When Dark Rag comes out, the Ult spawning AP cost and BP joining cost will drop, so maybe you can see more then. That's like 3-4 months away, CBA to check, it does read in the encyclopedia.
Rags? Outside of UE events, they're still being commonly spawned and shared. The most important thing about finding Rags is to have an active group of Friends and an active Union who also have their own Friends. And a Discord to announce it to others in the same Union/friendring. Currently, there seems to be a server wide panic about the T4 Soul costs, so Rags tend to fill up real fast. Things should settle down once people realize there's still a full year of farming time.The "which Soul should I use?" thread should answer that. Or the Second Anniversary recap thread.