Right. That is what I see as flawed logic nuno... If the chiller is set to turn on at 81 degrees, when it hits 81.2, its gonna kick in, and when it hits 81, its gonna stop. In theory, it is such a small change, that the amount of water actually chilled is very small.
The problem with an underpowered chiller is that working at full tilt, it can't cool quickly enough and the tank reaches high temp, or it has to work continuously to keep up. Which we agree on
I think what you are trying to say is that, with a huge chiller and a small tank, you are afraid it would essentially pump cold water into his display tank,because it was chilling the water so much. I don't know what the exit temperature on water from a chiller is or whether it is adjustable, but i'm willing to bet having a sump would essentially make this a mute point (essentially a mixing area, pre display tank).
A smart chiller would chill the water it touches to temperature X (81 degrees in this case) and this problem would not exist. My guess, and your assertion, is that it chills at full tilt until the thermostat turns it off, making a potential for cold spikes.