A wound track is a reasonable HP alternative. I mean, there's a huge difference between an HP system and no system, but the difference between an HP system and a wound track is not necessarily that significant.You could, except the games that implement static single digit hit points tend to have highly aggressive 'wound tracks' where each loss of hit points carries with it a commiserate debuff, which tends to change the problem from "every attack is save or die" to "every attack is save or suck". And while leaves you with some opportunity to respond, typically you have relatively few options to do so. They also tend to have mechanics that allow for more than a single point of damage to occur at once.
Even if the first wound gives the equivalent of Disadvantage on every check, that can present an interesting choice in terms of action economy, whether you hide from the fight (and thus deprive your team of a meaningful action each round), or risk serious injury in order to keep contributing. If you compare it to the HP system from 1E, where you didn't have Disadvantage but you died instantly when you ran out of HP, then it presents much the same choice. It's not quite a true Hunter's Dilemma, since there are a bunch of dice involved, but if every individual fled when they were first bloodied then the enemy would have a much greater chance of prevailing.