I've got a nice one recently: A pipeline has bytes being transformed to chars by a user selectable encoding, then the chars go to a next step.

In an AOT language, this must be dynamic dispatch, as there are multiple algorithms. The JDK, however, notices how the encoding is basically always UTF-8 and does an 'if utf8 then do utf8code else do dynamic dispatch'. Then the inliner comes along, pushes that if outside a loop, and merges the byte reading, encoding and char processing to 1 big code block, all optimized together.

Any optimisation transforms the program in some way that has to preserve its meaning. Generally, to do that, AOT compilers need to prove that the transformation is always correct; that can be difficult for some deep optimisations. OTOH, JITs can assume that some transformation is correct, aggressively apply it, and if it turns out they're wrong, the code will trigger some signal that will have the runtime deoptimise (some modern AOT compilers have some speculative and deoptimisation capabilities, but not as general as JITs').