"to protect the cyclist from the wind"

No, it's to eliminate aerodynamic drag, since nobody is strong enough to pedal against that anywhere near 180. It's awful hard to get a car to push against that. Nevertheless, going 180 mph on a bike is extremely dangerous. If you had any failure of the bike/tires, brushed against the slipstream, the towing vehicle suddenly speed up or slow down, you'd be dead.

I also expect the drag racer would need modification. They're heavily optimized for a few seconds at full power, not a controlled cruise at moderate power. You'd likely need an automatic cruise control setting for precise speeds, a much more effective cooling system, and a clutch that doesn't engage with a huge jerk.