Yeah I'm not sure that the number of classes is really what drives this. Rather simply that more people like to be the one doing the damage!

The tank is commonly looked to as the leader of the party, and as such the stress level and knowledge required there is often higher. Less people want that. Healers are seen by many as maybe unexciting, for girls maybe, gets blamed often perhaps.

How is tank vs dps vs healers in PvP? (I havn't tried that yet, but perhaps there's some motivation there to build dps classes?)

Either way I doubt that adding a new class to any of the category's will change this at all.