IMHO that is a bit extreme.
My campaign fixed the whack a mole thing with a couple house rules:
Any Crit: +1 rank of Severe Injury.
Downed to 0: +1 rank of Severe Injury.
Both stack so downed on a Crit = a Rank 2 severe Injury.
Possible to get 3 Ranks in one shot with rare special items or monsters that have an "great wounding" power. Like say a Vorpal Sword (but not on every strike!) or some high demons or undead.
Save vs CON DC 10 vs the Severe Injury (a variant of Lingering Injuries and my system is much less severe - see below). Success = -1 rank suffered. Crit Success aka Natural 20 = -2 rank suffered. Crit Failure aka Natural 1 = +1 rank suffered.
This dice for the Severe Injury Hit Location:
View attachment 143772
Severe Injury Ranks go from
1 (for a non negligible penalty)
2 (severe penalty)
3 (crippling: can't use that part at ALL anymore)
4 (completely lost that part, handicapped for good... or dead if it's head or torso... Do you want to roll a new PC?).
With a simple 12-entries "SEVERE INJURY TABLE"
Plus, any downed PC get Incapacitated status
until the end of the next short rest.
Finally I let stabilized PCs at 0 HP remain conscious if the player wishes. They can't talk loudly, perceive only things near them (15 feet), and can't take any real action except a single Action called "Last Ditch Heroic Effort" (max 1/Long Rest), which involve a CON Save just to succeed doing it, and then they take 1 damage and start dying again. I've found that this allows downed players to still feel as if they are still part of the action, instead of just watching the others play for what can sometimes be over an hour (for long fights asnd a Pc downed early on).
Ah, and Death Saves, it's an increasing d6 instead, +1 each round. Then
when First Aid arrives, or a healing spell is cast, the savior action is spent then the downed player rolls that number of Death Saves in one go, ahnd if he he still alive THEN the savior's action is resolved otherwise the healing just fails. This avoids the metagaming that "Oh Bob has been down 2 rounds already but we still don't really need to go help him right away because he already succeeded his first 2 Death Saves so he's probably going to be ok!"
Also, my Death Saves are d20 + Proficiency Bonus = way easier to survive!, especially at higher levels (I've had a rage quit by a player highly invested in his PC that evenntyally died). Some high level monsters can apply some (small) penalties to Death Saves, though. Lava or Acid pools can be more than deadly enough already. Plus, healing a Severe Injury goes beyond just slappping some healing and rest on it. Say a Rank 1 arm injury = disadvantage to attacks with that arm / can't use a shield with that arm. That sucks but at least you ain't dead and it will eventualy heal (albeit maybe not before the end of the current adventure chapter).
That gives a VERY strong incentive for players to avoid getting downed as much as possible.