So what's the answer to that?
How you make hit points, and hit point loss matter beyond that binary >0 or =0 determination while also avoiding death spirals?
If I wanted to do this, I'd take a cue from Fate.
In Fate, characters take Stress (not all Stress is physical damage), and have a small number of Stress boxes to absorb it - a default character can absorb three points of stress, a physically superb specimen can absorb 10. There is no penalty for taking boxes of stress. When you run out of Boxes, ou are Taken Out of the conflict.
If you've run out of stress boxes to absorb the stress, or do not want to take stress boxes for some reason, you can take a Consequence - a form of Aspect, that comes in mild, medium, and severe levels, to absorb more and more Stress.
Physical Consequences often take the form of a description of some injury - "Sprained ankle" or "Bleeding gut wound" might be physical consequences. The opponent may invoke these to give them a benefit (or the PC a penalty) on an action, or may Compel them to add a complication to the scene. In either case, when the injury is used against the character, the character gets a Fate Point.
Fate Points are the fundamental action currency in the game - used to gain benefits on dice rolls, power special abilities, and so on. So, while the character gets a detriment from being injured, it also gives them more power to do cool stuff. It matters to how the fight progresses, but isn't just penalties all the time.
In a D&D context, I might look to an extension of the idea of being Bloodied - being at half your max hit points or less. Maybe, when the character is Bloodied, the GM can assign Disadvantage to a roll, but also gives the character a point of Inspiration.