Several things come to my mind as an engineer who has designed cooling systems for industrial processes (and still remembers the basic equations). First, increasing coolant flow will require more energy. Since that energy doesn’t show up as kinetic energy (it doesn’t help move us), it will show up as heat, somewhere. There is a detriment in that fact, alone, but it seems likely quite minor to me within a typical realm of change. Still, it is a backward step on the energy balance. It is certainly theoretically possible to find a point at which increasing flow really hurts us, perhaps putting a water pump from a truck into a Volkswagen. This is not technically a problem of reducing cooling, though, but of increasing overall inefficiency.
The second thing is that increasing flow through the radiator will decrease the temperature difference across the radiator (coolant temperature returning to the radiator minus coolant temperature leaving the radiator). This is more likely to result in a higher coolant temperature, perhaps measurably so, but that doesn’t actually mean less heat is being removed. Heat removed is calculated by multiplying that temperature difference times the flow rate (and then times the heat capacity of the liquid, a constant value). When the difference drops and the flow increases, there are many mathematical possibilities for higher coolant temperatures giving actually higher heat removal, but it does introduce the possibility of confusing someone who is just looking at a single temperature gauge, particularly a digital gauge where small differences can be seen.
Third, increasing flow rate does not do much for increasing heat removal unless we initially had too low a flow rate and there was a lack of turbulence in the coolant flow through the system. In other words, increasing flow rate does increase heat transfer, but only to a point. Same goes for air flow across the radiator. More than likely, the engineers designed the flow rate well into the turbulent range, but we are talking about modified vehicles in most cases in this context so things could have changed from the engineer’s intentions. Putting on a larger radiator could be an argument for increasing coolant flow as I think those extra cores are typically extra parallel paths that could reduce turbulence through the radiator. The pump and radiator probably do need to be matched.
Residence time is not a factor in heat transfer calculations. The idea that the coolant doesn’t have enough time is a completely false explanation for what might be real observations at times in terms of temperatures.