This is more less nonsense, at least for batteries.
Of course if you only reduce current draw and keep the battery same that would apply.

Here it is the question of 10S vs. 12S heat generation when everything else is kept equal. That means battery energy capacity, size/weight, cell quality & grade, and battery age/condition. Good examples would be 10S 6000mAh vs 12S 5000mAh or 10S 5000 mAh vs. 12S 4200mAh. Those pairs have equal amount of energy capacity.
Now, compared to 10S equivalent the 12S cell capacity in the battery is smaller (by 1/6 or 17%) and hence has a bigger internal resistance (again in the same proportion). This results the stress on the cell is on the same level in both, 10S and 12S, batteries. The heat generation is the same for both. Please measure this and show evidence if you do not agree.

If you do not keep the weight and energy capacity same for 10S vs. 12S comparison then it is all useless. In a similar way I could say that 10S is better because I can use 10000mAh batteries and they do not get as warm as your packs. Not useful, right?

Truth is and is based on laws of physics, that to use 12S instead of 10S would call for change in motor/prop combination and battery configuration. These changes will counter the benefits that reduced current draw would bring. The ESC will benefit from reducing current draw and there you could go to one side smaller one in some cases.

You can also gain more efficiency by rewinding a motor to have more copper area in the winding. This will reduce internal resistance and improve efficiency with less heat. So, be careful, when you compare different combinations. It is not always clear which change causes the biggest benefits.