"No negative hp" seems like just such a stupidly bad rule to me. "Heal from Zero" is a bad rule for most sorts of D&D.
It's mostly just simplified bookkeeping.
Heal from Zero also makes waiting for your allies to drop before healing them a good tactic, kinda the flip side of focusing fire. Otherwise, it doesn't matter as much when you heal them, but not letting them drop might save them an action, depending on how initiative shook out. Heal from Zero thus slightly favors the players, as it 'wastes' monster damage, and avoids 'wasting' in-combat healing on a character who doesn't get hit for the rest of the fight.
No negative hps - just death saves & failed death saves for being hit while dying - is also just bookkeeping reduction. It really doesn't make much of a difference, but it means Healing from Zero, while negative hps can be healed back, or Healed from Zero.
But, neither are 'bad rules,' they're as functional (and as wildly unrealistic) as any other death/dying rule D&D has ever used, and simpler than some of 'em. And, like all 5e rules, they're just a starting point for the DM. Have to start somewhere, afterall.
If you want the advantages of Heal from Zero, you might as well go No Negative hps, and simplify your bookkeeping. If you want death at a certain negative hp total, you might want to do away with death saves or have a failed death save inflict a point of damage, instead of tracking them separately - but you can go with Hf/Z or not.