Thank you for the input!

We're talking about continuous collision detection here. And the reason I don't like capsules is because of this:

Right. This kind of case can be handled many ways. Often times player expects to slide off the edge if their center of mass is over the edge. This more or less matches intuition with real life. But for 2D games often times you want AABB-style "hanging off the cliff". In these cases a good solution might be to swap the capsule for AABB if the player is standing still or walking slowly, but capsule for general movement. Just sharing some ideas here.