Gyroscopic effect is not fully responsible for keeping a bike stable, but it plays a large part. You can experiment yourself, take a road bike wheel and a smaller wheel, spin it, and hold it at one end of the axle. The larger wheel will be more stable. Hold both axles and try to lean the wheel to either side, the larger wheel will be harder to lean. It is not rocket science. Ride a bike with small wheels, and one with full size wheels, and you will notice the difference in the effort it takes to turn the bars. It is not a matter of trail, spin the wheels with the bikes on a stand, and try turning the bars, you will notice the difference in effort.

I have spent time racing bicycles and motorcycles, and have felt the difference in gyroscopic stability when tires and wheels of different weights are used, though the steering and suspension geometry remain the same.