#Get Gritty As a bit of a frame challenge, it sounds like your table may be looking for some grittier realism with regard to healing and recovery - and 5e covers this with variant rules within the DMG without having to resort to houserules.

This doesn't mean you can't do the houserule, but you may be interested in some existing mechanics that may give your table what they're looking for.

The DMG Chapter 9 covers two major mechanics that are worth reviewing:

##[Slow Natural Healing][1] (DMG, 267)

Characters don’t regain hit points at the end of a long rest. Instead, a character can spend Hit Dice to heal at the end of a long rest, just as with a short rest.

 

This optional rule prolongs the amount of time that characters need to recover from their wounds without the benefits of magical healing and works well for grittier, more realistic campaigns.

##[Gritty Realism Rest Variant][2] (DMG, 267)

This variant uses a short rest of 8 hours and a long rest of 7 days. This puts the brakes on the campaign, requiring the players to carefully judge the benefits and drawbacks of combat. Characters can’t afford to engage in too many battles in a row, and all adventuring requires careful planning.

 

This approach encourages the characters to spend time out of the dungeon. It’s a good option for campaigns that emphasize intrigue, politics, and interactions among other NPCs, and in which combat is rare or something to be avoided rather than rushed into.

These rules/approaches don't necessarily resolve the bounce-back to consciousness in the thick of it problem, but they do look at what effect getting hurt badly may have on the rest of their day/week. [1]: https://www.dndbeyond.com/compendium/rules/dmg/dungeon-masters-workshop#Healing [2]: https://www.dndbeyond.com/compendium/rules/dmg/dungeon-masters-workshop#RestVariants

Get Gritty

As a bit of a frame challenge, it sounds like your table may be looking for some grittier realism with regard to healing and recovery - and 5e covers this with variant rules within the DMG without having to resort to houserules.

This doesn't mean you can't do the houserule, but you may be interested in some existing mechanics that may give your table what they're looking for.

The DMG Chapter 9 covers two major mechanics that are worth reviewing:

Slow Natural Healing (DMG, 267)

Characters don’t regain hit points at the end of a long rest. Instead, a character can spend Hit Dice to heal at the end of a long rest, just as with a short rest.

This optional rule prolongs the amount of time that characters need to recover from their wounds without the benefits of magical healing and works well for grittier, more realistic campaigns.

Gritty Realism Rest Variant (DMG, 267)

This variant uses a short rest of 8 hours and a long rest of 7 days. This puts the brakes on the campaign, requiring the players to carefully judge the benefits and drawbacks of combat. Characters can’t afford to engage in too many battles in a row, and all adventuring requires careful planning.

This approach encourages the characters to spend time out of the dungeon. It’s a good option for campaigns that emphasize intrigue, politics, and interactions among other NPCs, and in which combat is rare or something to be avoided rather than rushed into.

These rules/approaches don't necessarily resolve the bounce-back to consciousness in the thick of it problem, but they do look at what effect getting hurt badly may have on the rest of their day/week.