Didn't we already touch on this...
I don't want to explain why the class idea isn't a bad one at first glance the implied implication as planned (umm, yeah....) would unbalance the game further. Effectively reducing the gaming ability of half the classes either by rendering them even less effective over all or replacing them outright. In a game designed so each individual character is near hopeless outside of one or at most two niches this class will be overpowered simply because it fills such a wide role.
Not that the idea is bad, if introduced properly it, and a few other classes, could very well become a nasty addition to the game. Maybe focusing the dog so it is a flanking-melee style game play instead of quick-general roll it is made into now. That has yet to be covered solely, and effectively, by any single class so is a niche waiting to be filled. Reduce how useful this class is till it is on average with how useless every other class is unless properly utilised and I have no problem with it.
TF2 was, after all, one of the few games where everyone is equally as useless as each other... it is sort of the charm of it.
Personally: I think valve should work on a off shoot of Team Fortress. Expanding the game in newer directions then what has been seen so far, but keeping the cartoon and irrational nature of said game.
I think TF2 with vehicles that follow the same 'useless outside of a niche' system, for example, would kick arse. Imagine the wacky types 'top heavy' style of vehicles you could design and put them into a cartoon like world... it just fits! From Sidecar mounted bike that that a single shot seems to flip Indiana Jones style right through to tanks that look like a brick of steel on four wheels with a 16th century cannon which are just as useful as a brick of steel with a 16th century smooth bore taped to the top... yeah, potential?
It could also be a good time to expand on the classes, cause vehicles open up at last half a dozen potential new classes alone. Such as the mech-head for repairing and upgrade vehicles to make them even more top heavy you have to wonder if it is a good idea, the crewman cause someone has to know how to put a round into that ridiculously oversized turret, the speed freak just so we can teach the kiddies that meth and driving is not smart, and more non-vehicular classes like... the dog.