It is my view that if perpetual check were to become a loss for White then the White King should be given the ability to act as a pawn for capturing Black pieces (an ability which does exist in some variants).

If the rules were to change to make perpetual checking by White a win by Black then the balance has changed and it is no longer Black's objective to capture the White King but merely (a word used here to create emotional rather than rational effect) to stop the White King getting to the border. For me this is a significant reduction in the task for Black. Well executed this will also eventually result in the capture of the White King, poorly executed a win by forced perpetual check. There are certainly times when the perpetual checking can be stopped by Black by moving a different piece so the result is not always White's "fault". I can also foresee times when Black's move will be coloured by the expectation of containment giving a less aggressive and more containment approach rather going for the kill which, to me, is what Tablet is about. The age old struggle of fight (Black) or flight (White), not siege and fight.