Xjyuk

My understanding is that air resistance is where most of the pedal power goes to at high speeds, and that this is a concern not least for the wheels: What you pay for in a road bike wheel is aerodynamic and/or light wheels, not so much to other losses like rolling resistance and bearings.

So if air resistance is the thing to optimize a wheel for, the wheel should be tiny. Obviously in width, but also in radius, because even shortening the length of a surface reduces boundary layer drag. Has anybody thought of this?

Postulate: The faster angular speed of a small wheel is irrelevant to air resistance: If the forward speed is given, every point on the wheel at a given fractional wheel radius has a speed compared to the ground that is independent of the wheel radius. In other words, shrinking the wheel does not speed up any point on its surface; you just get less surface. Which should be good!

You also have to count for stuff you can get over - that's why 29-inch wheels are so popular with the mountain bike crowd these days. They suck at cornering, and that's why they came up with 27.5's. Smaller wheel diameters are great for accelerating quicker, hence the popularity of 650C wheel sets for triathlons. Scooters have tiny wheels because they ideally are ridden on paved roads or sidewalks, and can therefore get by without hitting any major potholes or bumps. At some point, people got together and determined an ideal threshold for wheel size that would prevent accidents by their sole ability to get over stuff. That's the best explanation I've got!

Assuming a bicycle with a conventional rider position, the rider cannot be positioned any lower because there has to be a certain amount of clearance between the cranks and the road. As wheels shrink, the frame has to extend downwards to reach the axles, so you are not really removing structure that causes drag, you are replacing it with something else.

Smaller wheels have higher rolling resistance, at some point that become significant compared to aero drag.

There are a host of other practical reasons, for instance:

As the driving wheel decreases in size the gear ratios have to increase to maintain the same distance travelled for a turn of the cranks. This is why folding bikes have huge chainrings.

Small wheels are less stable, as anyone who has ridden a Razor scooter knows.