I rarely ever 4B KK in this scenario, might be a leak, but I just get so little action from worse hands it feels like.
By calling I keep all his inferior valuehands in the pot, that too often fold otherwise, it seems to me.

Villain is very passive postflop in terms of barrelling. Yet, this board is so dry and normally I would never XR this texture in this spot, that I feel flatting is perfectly fine.

My exploit is to XR turns, to prevent him from XB AA and esp AK OTR. It's a very fishy raise size, but I feel it's the perfect exploit versus most players in this pool to ensure them stacking.

I tanked quite long OTR whether I should XC/XF or BET AI myself. My reasoning for jamming was that I expect him to jam some of his AA OTT versus the XR, but pretty much never with AK. More importantly, if I X, I expect him to XB with AK quite often.
The combination of these two led me to prefer jamming myself, to ensure stacking AK (and vs AA I will get stacked anyways)