Speaking from experience working on a social site with loads of signup flow experiments: the results are consistently wild. It's no competition on all the normally-valued metrics like interactions and retention.
*for some degree of "know" anyway. Better in most cases than "the news talked about this tweeter thing"
(edit: I do think they may have missed what might be the biggest boat sailing party, which was probably a mistake. But invite-only is quite reasonable.)
Threads solved the cold start problem by not having a personal feed at all at launch. There is only a single algorithmically curated one, prioritizing first/second/third/etc degree connections and otherwise showing content from everyone else. So the place always felt alive from day 1.
Nothing very special about those shortcuts. Had they had a standalone system, it's not be much better than all the other attempts. This is akin to how Snoy launched the playstation.
I kind of feel like Google was onto something with the "circles" idea and it's not clear to me why something like that didn't catch on. I don't want to share everything with the whole world. My college friends, my professional contacts, my family - these are all social circles that I'd want to be connected to with a service like this, but in separate buckets that don't overlap (or only somewhat overlap).
So from a user's point of view, exclusive/invite-only can be really appealing. But if you're thinking from a "make as much money for the company as possible" point of view then yeah anything that limits the number of potential customers you can attract is going to hurt.