The gyroscopic effect is not what causes a bike to balance, it's the arrangement of centres of mass around the pivot or steering. It is harder to maintain that balance at high speeds since small adjustments to the steering produce much quicker responses.
That's highly inaccurate. The gyroscopic effect is not everything, but it does get stronger at higher speeds. That's why even a simple wheel without any frame or steering mechanism will run mostly stable at high speeds. So when going at high speeds on a bike, it indeed is more stable than when going slow.
The article you link only claims that the gyroscopic effect is not everything stabilizing a bike.
Wouldn't balance actually be easier, due to the gyroscopic effect of how fast the wheels would be turning?