The third wheel does not provide any effective directional control at speeds exceeding around 25MPH on most GA aircraft, The rudder is controlling direction. If you have managed to keep enough weight on the third wheel that it can affect direction, you're already having an exciting ride down the runway! I agree that the Tomahawk is a bit of a special case, as the elevator has little effect in lifting the nose early, compared to other types, but it's still the rudder doing the steering.
To demonstrate yourself in a 150/152/172, do the following: Load it toward an aft C of G (but within limits, of course). Extend the flaps to 15 degrees, Find a runway or taxiway to yourself, ideally into a 5 to 10 knots wind. Hold the controls full nose up and open the throttle until the nosewheel comes off, then no more. The aircraft may have only moved a few feet before the nosewheel comes off - be careful to not get the nose so high that the tail tiedown ring hits the ground, that's really bad for them! Now you're taxiing with around 1600 RPM, at 15 MPH or so, with about the same directional control by rudder steering, as you would have were the nosewheel to be in contact with the surface.
Similar the taildragger, Heels on the floor - so not accidentally applying the brakes, stick forward once on the roll, so the tail comes up, and you still have lots of steering with the rudder.
Note that in Cessnas and taildraggers, there are springs which allow the third wheel to track the runway, rather than to move with the rudder. The rudder is doing the steering at speed. Piper nosewheel aircraft have direct steering, so some nosewheel scrubbing could happen with lots of steering on the runway, but it's still primarily the rudder steering at speed.