I've spent quite some time racing Downhill Mountainbikes - and believe me - the gyroscopic effect IS there - and it is very noticeable (DH bikes tend to have MUCH heavier wheels).
Riding lighter wheels has a lot of effect on acceleration and braking. Handling also improves ALOT with lighter wheels.
It also contributes to stability. But you do need to ride faster than this "wuss" (pun intended) moving at snail speed.