toucanbuzz
No rule is inviolate
If you go to zero at anytime, that changes and short rests now use the longer 8 hour time while long rests take a week. This persists until you get a long rest week.
Constructive criticism, mine would mirror the observations of @Ruin Explorer and @Blue . Hitting 0 happens often enough that I expect to see at least 1 player go down in a session. Could be bad luck like the DM rolling double natural 20s on the attack, or a bad save, but it's inevitable and unavoidable. As Blue pointed out, you're likely going to be punishing your front-liners, who probably rely on a Long Rest class ability. In a timed campaign like TOA or Red Hand of Doom, brutal.
Personally, I don't like "whack-a-mole" one bit and my gamers have voiced over the years it's silly. Dragon breath for 50 damage, down. Healing Word, back up. Dragon claw for 30 damage, down. Healing Word, back up. Goblin slits your throat (critical hit) when down, 2 failed death saves. Healing Word or a Natural 20 death save, back up.
For the last 3+ years, I've been using a homebrew Vitality system (suggested by a UA article). Rather than go into full detail, attached it (1p). Works wonders, fixes "whack-a-mole," and didn't create excessive down time. In gameplay, it's been a lot more exciting (player feedback from two groups). I've posted on my homebrew awhile back, so not wanting to derail the conversation about it. Just for OP (or anyone else's) consideration if seeking a solution to "whack-a-mole."