Sure, but neither javac (the Java to bytecode compiler) or HotSpot are doing that. The former tries to preserve as much as possible, and for the latter interprocedure analysis is too costly at run-time.

Could javac do the analysis and record it in the bytecode for HotSpot to optimize? Or is this kind of hybrid teamwork not done?

It is done, but for this case the problem is partial compilation. For this you'd need methods to be tagged as pure, but that assumption needs to propagate and it could be violated by a library being upgraded.