This is usually done automatically in Postgres in the background by the Autovacuum process. For high volumes of traffic or certain usage patterns you might have to tune the Autovacuum settings, or it might not be able to keep up with the more conservative default settings.

One issue is that there is some counter-intuitive behaviour here, if you see the Autovacuum taking significant resources, the worst thing you can do is to let it run less often. You actually need to make it more aggressive in that kind of situation, and/or fix your usage pattern or add more resources.

If a manual ANALYZE is necessary, this can often indicate a misconfiguration of Postgres, e.g. someone reducing the Autovacuum frequency or disabling it entirely. Postgres also got a lot better at this, so it also matters how old your Postgres version is.

Agreed, I never faced these issues as our database is relatively small but it's weird to see so many manual commands used for maintenance when these could be built-in PG ongoing process.

Why isn't that so?

It is built-in. The autovacuum process is doing this. When you have a large database you may need to tune some config parameters, as the default conservative setting for low/mid databases are naturally different.

Running these manual commands is just shifting the config tuning for large databases to periodic „manual“ operations.