The concave entry design was developed to hug the tire when placed in position before commencing the recovery. A tire is round, in an instance when you need to use a recovery board the tire is in a hole, so the entry of the recovery board needs to be optimized to have maximum surface touching the tire to ensure an easier recovery and less chance of wheel spin occurring when trying to drive out.
The convex board design runs out along the terrain rolling out of the hole your tires and vehicle are in. Then having the open dedicated exit gives the board better grip onto the terrain without the need for protruding grip lugs on the base and without these grips our overall board stacking height is a lot less. The board sinks into the terrain and the board design acts as the grip. Having an entry and exit creates a pocket between the board and the terrain which is why you then need the grip lugs on the base of a board.