I think this is not really inline with the philosophy of the main Lemmy devs. For this to happen, I think someone else would have to do the work of creating the random selection service. If it was popular enough, maybe they'd put a link on join-lemmy.org

There are differences between the servers, though. Instead of picking randomly, it should ask you a few questions about what you value and what you intend to do.

I made this account to look at NSFW stuff, for instance. I had read that lemmy.world was the biggest server and it checked all the boxes of allowing NSFW content, downvotes, community creation, etc.. "OK, should be fine." Only after trying it out did I realize that all NSFW thumbnails are blurred and you have to manually open each one, and lemmynsfw.com has a patch to fix that. So if you're making an account for that purpose, it should recommend that server.

Likewise, the admins of different servers have different goals and rules. beehaw is expressly created to oppose rationalism(???), for instance, and disabled downvotes and has heavy moderation of things that don't fit the admins' beliefs. The Lemmy sign-up process should give examples of the kinds of things that have been banned/moderated and ask if that's your thing or not your thing.

It should be kind of like https://chooser-beta.creativecommons.org/

(Also, server administration costs matter? Servers that are hosting lots of images will be more expensive to run. If you're consuming all that content with an account on another server, is that fair?)