Not your screen monkey (he/him)
Huh, can't comment on the post for some reason. Anyway...
My main problem with "count up from zero" is the way it incentivizes the cleric to wait until a PC actually drops before dishing out the healing. Let's say the cleric has a healing spell worth 10 hit points. If I get that spell when I'm at 5, it works as advertised. But if I get that spell when I'm at -5, I gain 15 hit points! I have often seen healers hold off on using their abilities for this exact reason.
I can certainly see that as a potential problem. It could encourage exploiting the metagame in ways that the PCs shouldn't be able to perceive or comprehend, particularly in a system with a large depth of negative hit points to exploit. If the limit were -10 like earlier editions, at least they'd run the risk of missing that window of exploitability and the PC is just dead.