I don’t think you’re wrong, but in all variants of it that’ I’ve seen it’s just been like. “You’re bleeding.”
“You’re dead.” before combat is over. Moreover I think it should do less damage, and more massive amounts of debuffs and the like, at least until a certain threshold.
I can’t imagine it would be too hard to add in a counter that (For now does nothing) as a placeholder say, 5,000 that ticks down whenever you take blood damage, and regenerates too after you stop bleeding. Just as a placeholder to get it to work, it would literally do nothing until some proper ideas are heshed out.