So if you pump water through the radiator too fast, it doesn't cool down as much, and then you start to counter your heat removal capacity gain from increased volumetric flow with the decrease that comes from using hotter water. Heat transfer relies on temperature differential after-all. So it's more complicated than saying "the more water you can push the better", because as with most things, there are trade offs.
Some cars do fine with no thermostat, because the radiator is over-sized and the increase in flow rate doesn't really lead to a coolant temp increase that hinders things. Some cars cannot run without a thermostat because it breaks the balance of the system and leads to a thermal runaway. There is no magic one line answer that solves all setups.
Former cooling system engineer here.
Remember that it is a system. You pump the water through the radiator faster, it doesn't cool off as much in the radiator, but it also doesn't heat up as much going through the engine. The net difference is that the coolant runs cooler, all things being equal. Q=m * Cp * delta T
Problem is, things aren't equal. The main problem is pressure. Without a thermostat, the pressure in the upper hose and radiator are increased. This can exceed their design pressure and leading to failures.
Increasing the flow rate may lead to hot spots in the engine and radiator, also causing unexpected failures.
Best practice is to keep a functioning thermostat. Will let the engine warm up quickly and maintain its temp.