I think you CAN get away with only physical and mixed sweepers. For instance, you can use 2 pure physical pogeys (Lets say Gyarados and Rhyperior, for example's sake). Then you toss in a few mix pokes. Mixape, Electivire and Kingdra allow for remarkably good coverage on both spectrums. Kingdra for example can Rain Dance/Waterfall/Return/Surf (Or Dragon Pulse, Draco Meteor, Ice Beam instead of Return or Surf). We all know how Mixape and Electivire work. Then the last one can be whichever you need, I'd think a cleric of sorts could work. That SHOULD work and be hard to wall. Kingdra and Mixape could take down Rhyperior, Electivire and Mixape have no problems taking down Skarms, Steelix doesn't like Kingdra and Mixape, nor does it like Electivire's quakes, same for any other steel/rock/ground wall.
So while a team does not NEED a special attacker, having a few mixed attackers is the least one should carry to cope with any high defensive poke.