A simple example: let program P do a zillion <something> * <command line argument> multiplications, and call the program every hour with argument value zero or one, depending on a coin flip. An AOT compiler would not even know that the program will never be called with other arguments. A JIT compiler could remove all multiplications.

Profile-guided optimizations only work on the next run, and, when used by the developer, do not work for cases where there are widely different usage profiles for a single program. For example, most users would have data sets that fit in memory, but others will have ones that do not.