There are other ways to add strategic deiversity than more characters, and excluding any gameplay consideration TF character lineup is close to perfect with strong, recognizable design IMO.
Having few characters also makes it a game that's easy to pick while making it easier to balance to keep it competitive, which plays a big role in TF2's identity in 2016 against bigger titles.
Thus TF3 would probably loose it's identity and audience by having more characters, IMO.

I see. What if they add abilities, though?

Or specializations and a passive skills tree, and more micro-interactions within the maps (doors, barrels, covers etc). Maybe micro-optimization in the form of animation cancelling on reload/recoil.

Those are interesting ideas. Especially the animation cancelling.