It matters a lot when it comes to handeling.

The angulur momentum of the turning bicycle wheels makes them act like gyroscopes to help stabilize the bicycle. This gyroscopic action also helps to turn the bicycle.
Having pointed to the gyroscopic nature of the bicycle wheel, it should be pointed out that experiments indicate that the gyroscopic stability arising from the wheels is not a significant part of the stability of a bicycle. The moments of inertia and the speeds are not large enough. The experiments and review of Lowell and McKell indicate that the stability of the bicycle can be described in terms of centrifugal force. A rider who feels an unbalance to the left will turn the handlebars left, producing a segment of a circular path with resulting centrifugal force which pushes the top of the bicycle back toward vertical and a balanced condition.

A bicycle held straight up will tend to go straight. It is tempting to say that it stabilized by the gyroscopic action of the bicycle wheels, but the gyroscopic action is quite small.

If the rider leans left, a torque will be produced which causes a counterclockwise precession of the bicycle wheel, tending to turn the bicycle to the left.

So now you know.