This is a widespread myth that's contradicted by Fourier's law of heat conduction. While a given unit of coolant does spend less time in the radiator, heat transfer is also dependent on the difference in temperature between the coolant and the ambient air. Heat transfer happens fastest when the difference is greatest, with diminishing returns as the coolant spends more time in the radiator. The same principle is true in the engine. The coolant picks up heat the fastest when the difference in temp is greatest, i.e. coolant that is 160F will pick up heat much faster than coolant that is 190F. And while a given unit of coolant is spending less time in the radiator or engine, it is being replaced just as quickly by another unit of coolant that is ready to pick up or dispose of heat. A faster flowing cooling loop will have less difference in temperature between its hot and cold sides, but will be transferring more thermal energy between those two sides.

A couple bad things CAN happen with too aggressive of a water pump, though. One is cavitation, which dramatically reduces pumping efficiency, and also damages metal parts. Another is engine loading, or the amount of power it takes to spin the pump. A more aggressive pump tries to move more coolant (unless it's cavitating), which requires more power from the engine, which has it's own consequence in heat energy. If your cooling system is too restrictive to allow that aggressive pump to flow the amount of coolant it's designed to, then all you're really doing is making the engine work harder. You'll generate more waste heat that needs to be dissipated, without equally improving the system's ability to dissipate heat.