I understand the distinction you're trying to make, but...boxing isn't just about "punching each other". ^^;
There are lots of other factors for a good fighter to consider: which arm your opponent leads with, what parts of their body they tend to guard, what kinds of punches they tend to use (i.e. what parts of their bodies they tend to leave open for a counterattack~).
And in the heat of an actual fight, being able to sense your opponent's state of mind and stamina will help you use your own energy wisely. If they're in an aggressive mood and you feel comfortable defending, you can let them wear themselves out for a few rounds and then strike when their strength is spent.
This is important stuff to consider in any fight, fantasy or otherwise; there's a 'baseline' level of strategy that a good writer knows how to employ when it comes time to challenge their protagonist in battle.
And I think it shows when writers don't understand that, because they end up doing what you described: creating a fight where the characters just "punch each other", without any thought put into it besides figuring out who the best puncher is and handing them the victory (or handing the other fighter a plot convenience so they can "turn the tables").
I don't think stuff like ^this is a particular classification of battle writing so much as it is bad writing that certain audiences accept as normal. =/
I'm gonna say a mix, I guess? I'm not really familiar with any series where the fights "focus purely on strength" (sounds kinda boring...) and I don't really know firsthand how Jojo does things...Although what you described sounds pretty solid, I also think that's kind of...how any battle series should be written?
Like, characters having to figure out how to overcome challenging opponents should be the norm, so I'm not really sure what to think when you write about it as if it's something specific to that series...
But anyway, I have no problem with power levels as a concept, which is where I think they're most valuable to the narrative.
An established ranking of the relative strength of your characters should be less of a tool the characters/audience use to somehow "calculate" their chances of success, and more of a tool the author uses to determine how much time and energy should be devoted to each fight, and to the buildup of each challenger.
For example, in The Last Airbender, establishing Azula as one of the strongest characters in the cast isn't just meant to tell the audience 'the MCs will have to get real strong to beat her'. Although they will need to increase their strength (and they do) the point is to tell the audience 'when the MCs finally have a real confrontation with this lady, it's going to be CRAZY' (and it was).
It's all about hype and payoff-- even if Team Avatar never got any stronger over the course of the story, a good writer would make sure they gained enough new skills and insight into her weaknesses to make for a really interesting, exciting final fight.
Aaaand that's why I tend not to write many battle stories, because I'm not good at the payoff. :6 I understand what needs to be done, but I just don't like doing it...I'm starting a new comic where I promised lots of violence, though, so I'm gonna try to get better. I'll have to...