I think it happened at slightly different times in different divisions. For heavyweights, the tectonic shift was Dempsey, tho the Willard model has never quite died off. Certainly Dempsey ushered in a new era, stance, attack, pace. He is the earliest resemblance of later modern heavies, or at least one mode of them. Tunney represented another mode, and I would say Willard represented a cruder incarnation of another yet a third breed. All three of these type last till this day. The Fitz and even Johnson we see on film, not so much.
Not sure on that, Benny Leonard should get more credit for that style than Tunney, perhaps even going back as far as Corbett.
I draw the line at whether a man can box/fight at all. It's nothing to do with what years he lived in. Boxing was always about hitting and not getting hit. Imposing your will on the other guy. Hitting the other guy hard enough to knock him out or outwitting him at every turn. Being able to absorb a shot when you have to. Having the heart to carry on and come back when things get tough. And being able to adapt your style to what the opponent brings. None of this has changed.