I have 11.5 size feet/shoes. The only time I experience this when my shoes are not clipped in and my foots are sitting to far forward on the pedals. This happened on my too small mtb and my now possibly too large CX framed bike.

Once my feet are locked into the pedals, I have never touched the tire. I do a few very low speed orbits at busway intersections waiting for the lights to change.

If you are experiencing this with platform pedals, try clipless.