That is a common misconception, which might apply to some JIT compilers. For example, OpenJDK does not only need to compile only the hot methods, but even then it employs tiered compilation, where more powerful optimisations are made over time, and so the JIT can take as much time as needed (it runs concurrently with the already-compiled program) and has more profiling information than available to an AOT compiler. I.e. the same optimisation might be much quicker for a JIT than for an AOT compiler because the JIT doesn't need to do as deep an analysis of the program.
The advantage AOT compilers have over JITs is that they don't require warmup and they don't consume resources at runtime, but JITs have a greater potential for optimisation, and AOT compilers generally require more low-level information from the programmer to produce good code. There are various projects for caching JIT output and get something that's close to the best of both worlds.
Having said that, compilers aren't all developed on the same schedule, and different ones might prioritise different optimisations.