Having played HS since roughly around the release of Blackrock Mountain, I can’t say I agree with your analysis of play style symmetry.
I don’t think I’ve ever seen a meta where the nine classes split themselves equally between aggro, combo and control. Indeed, to begin with, the model you propose completely ignores midrange, which lies halfway between aggro and control.
There have, in my experience, always been favoured classes in each meta, with the playstyle of classes shifting from one style to the next, depending on available cards.
Indeed, in the wake of Knights of the Frozen Throne and Kobolds and Catacombs, Druid was famously hated for having decks which played very similarly, but had different endgame styles (and thus required opposite counterplay).
This made me chuckle a bit. As far as I can remember, Priest has always been hated for this, long before DH was a thing. The only real exception being Razakus Priest (which was hated for being Razakus Priest).
Class identity being all over the place can be worthy of criticism, but I don’t really believe this can all be laid at the feet of Demon Hunter.
I would also point out that class viability can shift dramatically from one expansion to the next. Paladin is a prime example of this: it is oppressively predominant now (though less after the nerfs), but a few expansions ago it was extremely weak, with a class identity which was all over the place, each expansion having tried to take it in a very different direction, leaving it in a “master of none, sucks at everyting” place.
It pretty much took Scholomance to bring the class back to the front row.