D&D 5E House Rule Idea: conscious but Exhausted at 0 HP

[Charlaquin]

I don't see the strategic decision here - keep living or die?

If you concentrate on remaining conscious, you retain your ability to act, perhaps allowing yourself to deal that crucial final blow, to flee, to heal yourself, etc. but you remain an active target on the battlefield for your opponents. If you drop concentration, you are out of the action, but opponents won’t likely continue to attack you, since you are no longer a threat.

 

[FitzTheRuke]

I just kind of narrate the occasional 0 Hit Point creature as being conscious (and unable to do anything other than crawl slowly a few feet, or moan incoherently).

Heck, sometimes I let them scream out for a healer as they hold in their guts from spilling out unable to do anything else other than making death saves.

I do too. I pretty much have changed "Unconscious" to "Incapacitated" - No longer in the fight, but not necessarily blacked-out.