I'm seeing across various instances that registration is going through manual approval as an anti-bot measure. As someone whose also run Fedi instances, I know how bad the bot problem is.
I do think invite links can get around this though. If we allow existing users to simply send a referral/invite to their friends (and have a tracker on who is inviting who), that'll do a ton to both mitigate spam registration and allow people to join quickly.
The more obstacles we put in the way of registration, the more people will be dissuaded and go away. We've seen it with Mastodon (and now there's this whole reputation of it being too complicated). We have a window here to fix stuff if we're fast. People will eventually forget about the Reddit API and put up with it if we don't offer a compelling alternative when the iron is hot.
I'm considering making a GitHub issue, if anyone has any thoughts or plans to work on it, let me know. I have a decent amount of connections on the Fedi and if enough people are serious about getting this ASAP, I can help out with the logistics/coordination.
Another problem is that you never actually receive a confirmation if your application was received and/or rejected, you are just sorta stuck in limbo after applying.