What is the reasoning behind performance being effected as soon as the concaving sips below the edge?
I think when concaving dips below edge level, you are basically putting more wood at edge than between edge and middle (where it dipped below edge level), which doesn't make any sense as you either hit the ball off the middle or between edge and middle i.e. off centre. As long as concaving is above edge level, compared to convex shape with small edge (comparing at same weight/volume of wood available to work with), you are basically spreading out wood all along the way towards the edge resulting in a wider sweet spot compared to no concaving/convex back but with small edges.
From personal experience, i did find slightly concaved bats/modern bat shapes had wider middles compared to convex bats with small edges/old bat shapes. Not to mention, pickup is almost always better with concaving, maybe something to do with aerodynamics. Pickup difference can be clearly felt when trying horz bat shots.