[Goldeye]

A larger area does not increase friction.
However, it does distribute the force of friction over a larger area. Too much force on too small an area can damage a surface.

I'm pretty sure that's the principle behind ice skating. Your motion along the ice doesn't experience much friction because of its tiny surface area; the small amount of ice the skate blade is moving into simply breaks off the ice instead. However, when you are pushing your skates to the side or at an angle, the ice experiences less pressure and thus you are able to propel or stop.

In the case of skidding wheels, a larger area dissipates the heat generated better, preserving the wheel.