I picked Other.
It's No, but it's not "No, one more annoying thing to keep track of". It's "No, because it's a bad idea".
D&D is a team game. A character going down is rarely their sole fault, it's a team failure. A tank that was too good at their job of blocking all the foes and took too many hits so they go down. Or a tank that wasn't as good and let a foe get to a low AC & HP member of the party. A cleric that prioritized healing one party member over another and it was the wrong choice. Or just bad luck on getting critted or some failed saves. Having some sort of detriment to whack-a-mole healing (which is intentional in 5e) I can see. But having it last all day (or multiple days) affecting one player when they may not have had a lot to do with them going down is punitive.
But more importantly, front line is a valid and needed niche. Being willing to get hit and be in the fray, even if it's a heavily armored cleric who isn't using melee, is a definite thing in D&D. But, as the ones getting attacked the most they are the ones most likely go down to when luck runs poorly. You most often are punishing a player for making a choice to play a character that protects others. The melee battlemaster and the archer battlemaster are just as resilient, but one will be targeted a heck of a lot more. So you are handing out a penalty that discourages selfless play - that's the exact opposite of what I want to encourage at my table.
TL;DR: this is a bad rule that can target the wrong person, lasts punitively long, and works to make the table act less like I want it to. It's not just a "No, it's annoying to track", it's a "Heck No, it's a Red Flag about the DM".