Fediverse

no one has done an especially good job explaining why the fediverse is better than centralized solutions

The default example people use for "a federated service" shouldn't be Mastodon or Lemmy.

It should be email.

Why is it better that different companies, universities, and other organizations (and even hobbyists) can all set up their own email servers, rather than everyone just using (say) Hotmail?

1. If Hotmail does something you don't like, you can switch to Gmail or AOL instead, and you can still send emails to your friends on Hotmail.
2. Different providers can specialize in different things, while remaining compatible. Maybe one provider doesn't prioritize the features you need; but they can't prevent a competing one from offering them.
3. No one provider can impose censorship or other overextended control onto the whole system. No one provider can break the whole system when it has an outage: Hotmail going down does not prevent Gmail's servers from exchanging messages with the University of Tübingen's servers.
4. Different servers can operate in different parts of the world, under different legal systems. Not everyone is ruled by California or Washington state; or the US. A hobbyist operating an email server in Alabama is not required to comply with Dutch or EU law, and a hobbyist operating an email server in Amsterdam is not required to comply with Alabama or US law. People get to live under the law of their own country; and yet the Alabama mail server and the Amsterdam one can talk to each other.
5. The same infrastructure that supports federation also supports extension of the platform. Programmers can build services on top of email, and the medium is transparent to them. And, again, no one provider can tell them "no, you may not build that weird client program, bot, or mailing-list service." To be honest, you don't even get Hotmail if email is born as a centralized service. The whole emergence of webmail services could only happen because email is extensible and federated.