It should be noted however that the same can be expected to happen to the enemy too.
On average, considering a hypothetical fair fight between equal sides, both sides get wounded, therefore weaker. What weakness, it might be random: maybe one side gets weaker in attack, the other in defense. In that case, perhaps nothing changes substantially. If both get weaker in defense, combat speeds up, if both get weaker in attack, combat slows down.
But D&D combats aren't fair, each combat is stacked in favour of the PC because they have MANY combats to face. So the most frequent outcome of a single combat should be a death spiral for the monsters.
OTOH the injury can carry over to the next encounter (depending on the rules and the possibility of rests, of course). So rather than a death spiral during a single encounter, the expected effect is consecutive encounters becoming more difficult, until resting is available.
Does this sound bad? Well, aren't we commonly already designing encounters of escalating difficulty in each adventure?
An injury system will steep'en the difficulty curve of the encounter sequence, so it will require some attention not to feature too hard BBEG at the end.
Nevertheless, beyond average/long-term considerations, we should not disregard the possibility of a short-term risk. If the injury penalties are too large, getting injured
first can in fact doom the whole encounter. This is less of a problem for the PCs who are rarely alone, but if injuries are also too frequent then the chance that multiple PCs are affected increases.
These considerations lead me to be generally skeptic that injury systems last for long in most gaming groups. Because if you use an injury system you probably want to see people getting injured and significantly so, but for the system to be most stable they should be instead relatively rare and mild.