However, I don't see any reason why you can't just say that half of your hit points are health, and half are combat savvy. It doesn't have to be a top half/bottom half sort of thing. If you get shanked by a surprise attack with a poisoned blade, that is physical damage, buster. That's coming off the top. That sword blow to the gut? Yeah, it's mostly physical, but there's a real pain that lingers, and that makes you want to quit. It's drawing upon both sides of the hp equation at once. And that dragon breath that you made your Feat to resist but still suffered 15 hp damage? Yeah, that only singed your beard, but MAN are you ready to throw in the towel after that.
Why is this important?
Healing. Recovery. Down time.
You see, I don't like down time, but I also don't like a lot of mechanisms to resolve it. However, in a short period of time (no, I'm not calling it short rest), you can recover your willingness to fight, your moxy, and your breath. Sit down, have a drink of water (or something stronger), get a talking to from your friends, make sure your sword isn't broken, and you'll be good to go. You also recover up to half of your total hit points.
That bloody wound on your leg? That's going to take some time. Bandage it up all you want - you need to rest it for a while or get some supernatural healing. That falls into the 'other half' of your hit points.
So, as a hero with 20 hit points, you will recover up to 10 by resting for 1 turn. You only took 7 points of damage that fight? Great. You're good to go at full hit points after resting for 1 turn. You took 15 points? Sorry, bucko. You can get 10 back, putting you at 15, but that last 5 is going to require a good night's sleep, a potion of healing, or a friendly cleric. The fight that took you right to your limits and dropped you to 0 hit points? You can get back to 10 after resting for 1 turn, but that other 10 reflects some deep wounds and severe bruising.
Yeah, this leans more towards 5E, but I think is a bit simpler, and is something I'm going to hard-wire into the mechanics for Sentinels of Echo City.
For me, this mechanic didn't originate in 5E (or even D+D for that matter)... as I was working on a wrestling RPG 20 years ago, I was thinking about how to reflect the recovery that wrestlers get when they tag out in a tag team match. A guy will be borderline out, ready to be pinned, and tag out. He rolls out, exhausted, collapsing on the floor. However, 30 seconds later when he's tagged back in, he's good to go, fresh as a daisy, and ready to rumble. Superheroes can do the same thing. Give em a few minutes, and they are ready to go back to work. This also helps to offset the fact that opportunities for healing are few and far between in a superhero game, and when you change scenes, supers are generally back to full health (or very close to it). They are more likely to be at or near full capacity when they hit that final showdown with the super-villain.