It's funny, because for racing, 1/8 and 1/4 mile at least, you can have a really CRAPPY cooling system, since you're not running that long. In fact, run on methanol and throw the radiator in the DITCH. ON THE STREET is where you need the BEST cooling system you can build for a high performance engine. PERIOD.
I'm not going to agree 100% with that. "best cooling system" could be defined in different ways depend on how you score it. But I'll define it as the cooling system that has the potential to remove the most heat.
A performance car driven on the street is not being "exercised " vigorously for long length of time. Like in your example of a drag car not needing a heavy-duty cooling system. Performance cars driven on the street are given an occasional burst of speed while most of the time just cruising along. The btu's produced under cruising speeds are far less than when the engine is under full load.
Where some street cars struggle is at low speed, stop and go or at Idle. The engine doesn't produce more btu's under these conditions instead the cooling system becomes less efficient. Low coolant flow because of low engine speed and low air flow because now you are relying on the fan only for all your air flow. No additional help from air flowing through the radiator like it gets with the car moving at speed.
In my opinion where cooling systems are really put to the test is in applications where high numbers of btu's are produced. High power engines operated at high load over a long period of time. I think of endurance racing for example. These are very robust cooling systems. Driving a performance car on the street in the same manner they are driven on the racetrack will likely land you in jail and would for many result in an overheated car.
I won't get into vehicles that tow heavy loads on the roads and streets but those too have very robust cooling systems.
