What’s the square cutout I saw on car bumpers?

The big rectangular inserts are often for hitches too.

It doesn’t make much difference. They’re not for towing so wouldn’t normally be used while moving, but I’ve towed and been towed by off center tow hooks and it only pulls to the side slightly.

Look at the front of a 4WD truck sometime. They generally have an off center hook on the front end of one of the frame rails, and a tie-down loop on the other.