Scooters and skateboards are obviously meant for slower speeds, below 5 MPH. Typically if you go faster than that, it becomes harder and harder to control the scooter, and you will fall off. An example of this is the speed wobble, examples easily found on youtube.
What's the deal? Why is it that comparatively, bicycles can handle higher speeds with more stability and comfort?
As has been mentioned above the size of tires plays a major role. Let's assume the manufacturer standards for a wheel after improving the shaft allows 1/100 mm of play. This much play would encourage a small wheel to resonated while shimmying much more than a big wheel which would need much mor time to complete one turn.
A 10 cm diameter wheel at 20 km per hour rotates roughly 10 turn/ second which is much closer to its natural frequency of vibration around the shaft versus a large wheel which takes ~1 seconds at the same speed. Also, the small tire has a very small I, moment of inertia WRT the shaft axis so it will bounce around easier. $$ \omega_p = \frac {mgr}{ Iw} $$
Precession is inversely proportional to the spin of the wheel speed meaning the small wheel will precess much faster and because it needs much less play at the shaft to wobble, it will resonate and shimmy.
There is less gyroscopic effect but this is not as much a factor. It is camber of two wheeled vehicle that is self correcting. If you push a bicycle backwards it will not stay up.
With the smaller radius the rpm is higher. If the tire is out of round it will wobble. They often put cheaper tires on a scooter and / or do not balance them.
Smaller wheel base makes them less stable.
Racing scooter attain high speeds.
I agree that wobble magnitude vs. wheel size is a significant source of instability.
My suggestion is that another major instability source is the relative lateral acceleration in a turn compared with your ability to compensate. The center of mass is very high on a skateboard, compared with the wheel axes, so a little centripetal force leads to the CM going "outboard" and causing a crash. By comparison, not only is the CM of a bicycle much closer to the wheel axes (in height), but you can force a far greater out-of-plane tilt on the wheels to correct against that centripetal force.
The smaller the wheel the less gyroscopic effect is created. Death wobbles can occur at slower speeds with smaller tires. Taller tires is what gives motorcycles and bicycles their stability compared to the smaller tires of a scooter as the speed increases.
To enlarge a bit upon Carl Witthoft's answer, which I upvoted, remember that the swivel mechanism in the skateboard's wheel trucks is designed to provide a certain (fixed) amount of steering action for a given amount of board tilt. At ordinary board speeds (a brisk run) the board tilt provides the rider with approximately the right amount of lean angle to make the turn coordinated (as it would be for instance on a bicycle in a turn).
The rider has no way to decouple his lean angle from the board tilt angle to produce a coordinated turn at speeds different from the board's "design speed"- meaning that at slower speeds, the rider will tend to fall towards the inside of the turn and at greater speeds he will tend to fall towards the outside of the turn.
At high speeds, fighting this tendency puts the board into a speed wobble in which the upper part of the rider's body does not track the movements of the board while the lower part does. Mayhem ensues.
Wheels surface area is very, very small, compared to say a bike, tricycle or other wheeled vehicle. That's fine on hard smooth surfaces like say a roller rink or a skateboard ramp. But terrible on pavement and gritty surfaces. Rubber wheels slightly deform and compress to meet the surface contours they ride on. Hard wheels like skateboards and rollerblades do not. So the weight energy applied to the wheels doesn't cause it to grip the surface very well. The more surface area you have to adhere to a surface, he safer it is at high speeds. Case in point look at a standard automobile tire's thickness compared to a race tire.
You can use a 'negative' rake to increase the stability - like this: https://youtu.be/oprWwrEmjmI
It even works without handlebars: https://youtu.be/5MQ7qDzfENo
Or if you want suspension too: https://youtu.be/ECzFlrXNry8
... sorry about the volume of the music!
