The obvious ones - that it’s not controlled by a single company, that you share data between instances.

No central entity deciding what you can and cannot see or say

Well, these don’t really apply to Lemmy or fediverse microblogging, but interoperability and censorship resistance. These mostly apply to things like XMPP and standards of federation that are widely adopted.

Im honestly not a fan of federation the way Lemmy and mastodon and the like do it, because the servers aren’t really communities truly, theyre interchangeable choke points in an amorphous blob. The servers are just there because that’s how they built it and aren’t really a positive with regard to UX. But, in a system where different servers focus on themselves first, like forums for example, where the users primarily use them to interact on their server, federated architectures enable communication between these communities and that’s great. That’s how I use Lemmy; I’m primarily on the server I want to use and interact on, and I venture out and engage with others on other servers, but that’s not how most people use it, they just pick a server and everything after the @ is meaningless, they’re here for the network, and a federated model is not conducive to good UX if the network is the draw.

For things like the fediverse and threadiverse as it’s been named, where the network itself is the draw and not the server in particular, I much prefer a nostr like architecture where the servers have little to no bearing on participation and just relay posts and other interactions.

One way monopolies form is through economic efficiency. One major cause of that efficiency is positive network effects. Network effects are the economic effects multiple people gain when they use the same product as one another; this is particularly obvious in social networks, which get to be more fun when your friends use them, or when cool, smart people use them to create guides, stories, videos, music, etc. that you can enjoy. Social media tends to suck when there aren’t many people on it, since nobody’s really talking about anything you want to talk about, and if you post a lot, you feel like you’re shouting into the wind.

However, competition and variety are still good things. They still help advance technology, and help keep firms honest. Monopolies take advantage of their consumers, because they can. Because they have no competition.

Is there a way we can have competition and variety while still taking advantage of positive network effects?

Yeah, federation. Extend one network across any number of services that want to participate in the network. The network can grow arbitrarily big, while the market remains competitive.