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.

So the real question is, why is the upgrade process so incompetently designed, and why has no one fixed this?

I think one really BIG factor is that built-in logical replication wasn't introduced until PostgreSQL 10 in 2017, before that you only had physical replication for master-slave but iirc that didn't work between versions so doing a "hot" upgrade was more or less impossible without third-party tools iirc.

So even if it's available these days, the amount of people still subjected to upgrades from older version still leaves an impression that it's really bad.

There is still major issues with logical replication, mainly limited feature support.

What's lacking? Specific types or schema changes?