Not quite so sure that they have as much of an identity as you think they do. Last year, Bledsoe's injuries for a lot of the season sort of forced them into being a Goran Dragic-driven, run and gun team with a scrappy guy inside (Plumlee) and a bunch of perimeter dudes outside, regardless of size (Frye, Tucker, Green, Marcus Morris).
Now obviously quite a few of those shooters are on the team again this year but now Bledsoe is (temporarily) healthy and they added IT to the backcourt. Now, while both those guys are not horrid perimeter shooters by any means, they're far more ball dominant than, say, Channing Frye, who would just sit around behind the arc and wait for someone to pass him the ball. Now you could obviously ask IT and Bledsoe to be change their games to fit last year's schemes but that would mean essentially taking away what made these guys good NBA talents and turning them into just-okay level guys. Which, given how much money is being invested in that backcourt, isn't ideal.
I'm not saying they're going to flop or anything. Just saying that it may not be quite as clear-cut as you seem to be characterizing it. (Also, IT took more shots per game than both Dragic and Bledsoe did last season so that'll be fun to watch)