[Since87]

The reason people get optimal cooling at a voltage below the pelts maximum, (Vmax) is that the power consumption of the pelt goes up roughly as the square of the input voltage. At about 75% of Vmax, you are getting 90% of the pelt's heat pumping capacity. (Q)

Running the pelt at Vmax instead of 75% of Vmax means putting 78% more power into the pelt to get 10% more cooling.

That extra 78% power consumption has to be cooled by the hot side cooling system. The hotside cooling system (and thus the hot side of the pelt) is going to get hotter because of the increased power input. Even though you get a slightly higher deltaT across the pelt at Vmax than at 75% of Vmax, most hotside cooling systems will allow the hotside temperature to increase such that the additional deltaT is cancelled out or worse.

I've attached a crude paint drawing that gives a rough idea of these issues.

Edit: Don't take these curves too seriously. The power consumption curve should be exponential, and the cooling capacity curve should be parabolic. I was too lazy to generate accurate curves with excel.