Why does everyone run ancient Postgres versions?

Because the actual process of upgrading Postgres is terrible.

I say this as someone who absolutely loves using it, but the actual process of upgrading Postgres is something that takes significant downtime, is error-prone and you're often better off just dumping all the databases and reimporting them in a new folder. (A good idea in general since it'll vacuum and compact indexes as well if you do it, combining a few maintenance routines in your upgrade path.)

It requires having the previous version of Postgres installed, something which can mess with a number of distro policies (not to mention docker, which is the most popular way to deploy software that will typically rely on Postgres), and unlike most software with that issue, Postgres is software you want to be managed by your distro.

Therefore, most people only upgrade by necessity - when their distro forces the upgrade or the version they're using reaches EOL.

I'll confess - I have a project that uses Heroku's managed Postgres and my preferred upgrade method is to set the maintenance window to the middle of the night, create a backup, and be awake at 1am to make sure that nothing is broken after they force the upgrade. Their auto-upgrade process hasn't failed me so far, but there's no way to manually trigger it.