If it was gyro, you couldn't turn corners
There is a physics story about a travelling salesman in the USA who, to enliven his dull routine, would check-in to hotels with a powerful gyroscope in his suitcase. Watching the bellboys deal with an object that "fought" when it was turned was a real hoot, apparently.
if your bicycle wheels truly were strong gyroscopes, there would be horrible cross-feed between tipping the bike and turning the front wheel...