Higher water flow almost always (except in some extremely rare circumstances) results in improved liquid thermal convection, meaning solid to liquid (or liquid to solid) heat transfer.
It's impossible for the water to be flowing too fast for it to not pick up heat. What happens is that the faster that the water moves, the more turbulent it is, and therefore the better the heat transfer.
Yes, if the water runs twice as fast as before, then the water only has half the time to pick up the heat, but by the same token, the water circulates twice as fast. As a result, the water spends exactly the same amount of time in contact with the radiator regardless of how fast it's flowing, but the faster it flows, the more turbulent, and therefore transfers heat better.
Higher water flow rates are better. True for radiators. True for water-blocks.
What can happen though is that as you stick a more powerful pump into the system to boost flow rates, that more powerful pump will add more heat into the water than before, and as a result the extra heat may overwhelm the benefits seen by the higher flow rates. This is however a different topic.