Large corporations are probably the worst place actually. You get slotted into some random project treadmill (which will be completely different from whatever position you interviewed for) where most of the decisions are made by middle managers at least one or two levels above you. Going out of your way to solve problems will be ignored at best and my even result in a reprehend.
These places are for people who hate thinking but are good at pretending otherwise.
Top Talent won't be leveled such that PMs can be 1 or 2 levels above. They'll be high enough that the project plan heavily consults them from inception.
These places are for people who hate thinking but are good at pretending otherwise.