TYPO3 Core

It's impossible to cache menu generated using MenuProcessor.

MenuProcessor Configuration contains invalid Arguments: cache.

Processing HMENU is an intensive process especially with expAll=1.
Using MenuProcessor actually means that the menu is processed at each page call (if the page is not yet cached)

Also, since actually MenuProcessor hard-code ACT and CUR, it could be useful to implement a feature that automatically caches the menu without ACT and CUR and then it overrides the cached menu, setting ACT and CUR over the cached menu.
See: https://gist.github.com/julrich/d91c1ac1968418e6ae8290f2a2e90afb