A quick search through your post history shows that even you consistently refer to WAR's 'self-healing by attacking enemies' as life steal. So I'm not sure what we're basing this new fictional explanation off of, even if you manage to successfully fabricate one just for the sake of the argument. If you want WARs that heal themselves by hitting things, that's perfectly fine with me. Perhaps every time they punch someone, they make their opponents drop potions, bandages, and medkits that you can pick up. But that should be part of the visual storytelling of the action itself.

Like I've said multiple times, I have no problem with Thrill of Battle. I actually think that it's thematically great and could easily be the basis of WAR's identity. I'm a bit iffy on Equilibrium, primarily because the naming choice is somewhat random. But you could convince me that perhaps it's something thematically similar to a Second Wind type effect. I just don't get the lifesteal bit. And there's nothing in the visual storytelling of the actions that explains it how a barbarian is capable of absorbing someone's life force, potency caps on life absorbed aside. You might as well give them sparkly spell casting and pretend that it's not holy magic. Er, that's, um... the physical manifestation of channeled rage, not magic! Maybe give them Bio Blaster while you're at it too! Oh, that's not poison coming out of a machinist's tool, that's, er... angry flatus! Good work.

HP boosts in this game are a functionally better version of flat damage shields, because they translate into a shield + heal. That's why Thrill is on a longer cooldown. You'd actually need to be careful to make sure that it's not too broken. That being said, I can tell you for a fact that players found comparing massive HP pools to be ridiculously good fun. And I think that designing jobs in ways that make them all individually feel fun to play should always be a priority. And that really comes down to identify the visual story that you want to tell through each job's ability set.