... I assume the peak heat at the beginning is the reason then with lid on it settles in. ...
Sounds right. Consider that when deep fried, they get hit with high heat immediately, all over, no let up. Grilled, while one part is getting high heat the other side of the meat may not.
So by the time you flip or whatever, that lower-heat skin is already cooked enough that "more heat" isn't gonna render the same crispness as the immediate attack did to the other part.
I submit that's the reason why it's hard to get chicken skin crispy any "normally grilled" way, especially if not battered, even if you try to "reverse sear" them.