Why does everyone run ancient Postgres versions?

Databases tend to be "stickier" than other parts of any large software system. Largely because database migrations are costly. You can't just tear down an old database and rebuild a new one, you have to figure out how to move all that data across too.

The consequence is that things in database-land tends to move slower than other types of software. This I think is the major reason why we still use SQL.

Have postgres updates actually been requiring users do migrations? Or is this just a fear that something will go wrong?

Well if it's self-hosted you have to do it yourself. You can either backup your databases from the old version and restore it to the new version once installed, or you can use pg_upgrade to upgrade/copy a old version data directory to the new version.

I don't think this is done automatically when you simply install a new postgres version, but I'm not certain of that.