The main game I'm working on, Downforce, has a somewhat usual focus - car racing! - so this might be a little less relevant. Or maybe more interesting, who knows?
When it comes to player characters, it aggressively rejects tracking physical damage to player characters. To quote myself:
Damage to cars - sure, but when it comes to their drivers it’s just not really the focus of the kind of stories this game is telling. Putting a character in hospital stay after a crash should be a major plot development and driving fast enough to make eyes bleed definitely shouldn’t be something to penalize.
Even if a driver does get hurt, hell, take a look at Niki Lauda. The injuries from his near-fatal 1976 crash at Nürburgring had been severe enough he was given last rites at the hospital. Yet in the end, he only missed two races and competed again mere six weeks later at the Italian Grand Prix where he took fourth place, despite the burns on his head still being fresh enough to bleed.
The closest HP equivalent Drivers have is Stress - a sort of temporary stacking debuff, indicating the mental pressure they're under. It's mostly about what it says on the tin and all physical injuries are just subsumed into it - treated just as something to persevere. It doesn't matter where Max Payne got shot, it only matters that he's popping pills, you know? Stress mechanics follow this mental state logic - you can just try riding it out or cross out one of your personality-based stats (such as Boldness or Teamwork) to ditch Stress quickly. The recovery of stats erased this way is dependent on achieving personal goals. In a (hopefully) cute touch, the stats are organized in opposed pairs and you don't necessarily have to recover the exact one you erased earlier own - maybe you regained your confidence to get that Boldness back, or learned your lesson and started approaching the track with more Composure?
Knowing that the above will be insufficient for some games (looking at you, inevitable post-apo death rallies), an optional Wound mechanic has been provided - but it's basically just a way to repurpose another mechanic from the system to put a number on the physical harm, to tell you when's a good time for some badness to happen or the player to finally get knocked out.
As for the cars (which essentially comprise half of one's character sheet), they suffer Strain. This term had been chosen to encompass actual-getting-tailboned-damage and the general wear and tear of high performance competition, such as burning rubber or choking the engine past its limits. It's essentially attribute damage suffered by car and is intentionally open to some interpretation - is a worn tire impairing one's acceleration, speed or grip? It's meant to go for the end result of damage and let everyone be a little loose with the exact justification.
This ease of interpreting fiction is something I believe to be quite important for the subject matter. With car action being the game's legitimate focus (and not just a throwaway coat of paint over some mushy storygame), I believe a race has a lot of rote maneuvering (in the sense where ttrpg combat is generally rote), but once it goes off the rails, it goes there hard - y'all aware what Ross Chastain pulled off in NASCAR earlier this month? So it was important to me to build a framework ensuring the right inputs and outputs and thus allowing you to easily bullshit a little about the exact throughputs.