As I believe I mentioned earlier in this thread "Bicycling Science" third edition by David Gordon Wilson is an excellent reference for many questions on cycle physics and technical information. It is published by MIT press and is available on Amazon for a reasonable price, under $20.

If you want to experiment try a bike with locked steering and see how unrideable it is. Back in the days of friction steering dampers on motorcycles I tried riding with it overtightened and it made the bike very difficult to control. The minute steering corrections done automatically to control machine balance could not be done readily with the tightened down steering damper. The whole bike felt out of control, not a safe feeling.

This was true even at speeds well above normal bicycle speeds and with wheels and tires much more massive than on any bicycle. These should have provided much more gyroscopic force if such force actually aids stability, which according to the above mentioned book it does not.

Tried on both a 1967 Triumph and a 1972 BMW so engine layout and orientation did not change the result of the overtightened friction steering damper.