What would happen if ultralights had mountain bike style treaded tires? What would happen if ultralights had off road treaded tires?

Mountain bike tires are made for going off road through mud, etc.  They have voids between the tire lugs to clear mud etc.

Why not off road going airplanes? 

I assume the reason is, the lugs would catch air and start the tire spinning during flight? 

Is this correct?

Or is it just a drag thing?
Mountain bike tread is meant to sink into the mud in an attempt to gain traction on firmer ground beneath the mud.  A plane generally doesn't want to sink into the ground (even during braking), if it sinks too far during landing or take-off, the airplane is more likely to catch the forward gear and flip/strike the prop.

Bush plane tires are designed to land on soft fields.  The difference between mountain bike tires and bush plane tires is that the high surface area of the bush plane tires attempt to "float" on top of the soft ground rather than dig into it: