> I think it was hotspot that first does interpretation, then - when interpretation proves too expensive - switches over to a quick jit. And when code gets executed lots of times it runs jit again, this time with deep optimization settings.

This is configurable, Hotspot can JIT right away when application starts, but then be prepared to wait a bit.

> What I personally don't understand: Why don't we cache JIT results between runs?

They do, just not the OpenJDK that many only care about.

All commercial JDKs support code caches between executions and AOT compilation.