Why aren't road bicycle wheels tiny?
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.