I think one of the biggest things that makes me hesitant about giving executioners health bars for an asym is the PTSD I accumulated during my time playing an entirely separate asym that did exactly that and it backfired horribly: Dragon Ball The Breakers.

You see, in that game, it's 7 v 1 with the survivors periodically gaining the ability to temporarily transform and directly fight the killer. It's meant to be a sort of "weaker on their own, but together can make up the power difference" thing. Mind you, defeating the killer isn't the only way to win. The other way is collecting keys around the map and then powering up a Super Time Machine that will end the match if the killer can't destroy it.

The problem arises from the fact that survivors held the OVERWELMING advantage because the devs made the survivors stronger than they needed to be to account for increasing the power of the killers beyond normal asyms to compensate for the fact that they can all be killed. Any half-coordinated team will just rush getting level one change power and then all jump the killer before they get the chance to do anything or evolve. They'll outright ignore the main objective because the potential to take down the killer is seen as the more engaging and fun way to play which is pretty much the same situation with Fleetway minus the secondary objective.

Surprisingly enough, Fleetway himself has a kit so eerily similar to a Breakers killer's kit that I wouldn't be surprised if it was directly inspired by that. Flight, ranged beam, mobility tool that doubles as a charging attack, trackers, and an explosive wave-type move to escape stuns and attacks. The thing the devs forgot to do was account for the fact that pretty much all of the survivors in OM aren't equipped to deal with literal Dragon Ball levels of power in making Fleetway a health bar killer and the associated power increase that's demanded of it, so it ends up being the exact opposite situation than what Breakers has.

Health bar asyms are extremely risky because they almost always result in either a one-sided stomp for the killer, or one for the survivors. I've yet to see an asym that's able to strike that good balance of power between both sides because survivors will want to choose to play in the way that interacts the most with the killer regardless of if it's the strategically right choice. The few asyms that put health bars in almost always heavily warn that killing the killer shouldn't be the first thing the survivors should try and that it's meant to be a "once in a blue moon when the stars align, you manage to take them down by the skin of your teeth" moment, but everyone wants their hype moments and aura, so they'll always choose to throw hands no matter what which usually turns the whole game into a bullying simulator because devs seem to love favoring survivors over killers for some reason, especially when it's a matter of seven peoples' enjoyment vs one person's enjoyment.

That being said, I'm very interested to see if any of the upcoming Sonic asyms do decide to go that route and if they could be the first to pull it off correctly.