E.g. OVH, Hetzner, TransIP... idk whatever kinda server you like. Or repurpose an old laptop at home, for a few Watts you get something that's usually more powerful per ¤ than a VPSes (or "cloud instances" in newspeak). Then install a Matrix server, add your domain, and you've got your own Signal alternative.

Or just use the standard matrix.org home server if you're just trying it out / don't mind a not-super-fast home server. Or one of a dozen public Matrix servers: https://www.hello-matrix.net/public_servers.php

IRC all over again. I don't see this taking over until someone comes up with its Gmail.

'its gmail' is matrix.org. It is the default server when you start up Element.

Exactly. There's no reason to run your own server aside from supporting the decentralized nature of it (or wanting to be 100% in control).

Your own.

Then it's dead on arrival.