I think it's worth the effort just to make sure you keep familiar with the process for upgrading (including making appropriate backups). It's pretty quick and easy to upgrade and makes sure you're on top of deployment for your project.
No real advantage especially with a mostly idle system.
But it's a good idea to keep up with the versions anyway. The upgrade processes isn't really complicated and if you can afford a downtime not really challenging.
In my experience it's typically easier to migrate from version x to x+1, rather than waiting a long time and then migrate from x to x+5 (or similar big jumps).
But regardless of the strategy for major version upgrades (10 -> 11 -> 12) you should at least keep up with the minor updates (10.1 -> 10.12)
Even if you don't want to upgrade to major version as you don't need additional features, it is advisable to upgrade to latest minor version of PG-10. See docs https://www.postgresql.org/docs/release/ for the latest releases and what is fixed in each minor release.
I've got pgBackrest set up for backups and pgBouncer for connection pooling set up so it's a case of wondering if there is some benefit to the newer versions for someone using it "casually"
Since it's require quite a bit of reconfig and testing.
Also the server the DB is on is RAM constrained. And Postgres making a process per connection brings it right down versus using pgBouncer to pool connections.
It seems complicated but it's actually quite simple.