High ceilings help when you don't have air conditioning. They are nice aesthetically but unnecessary and even detrimental (more air volume to cool) when you have it.
High ceilings not only avoid the need for air conditioning (my home has 11' ceilings and no air conditioning), they make you feel better in the space. When I am in a building with low ceilings I feel totally claustrophobic and tense - this is not something I want to feel in my own home.
Feels like nitpicket but: volume of air is in itself not a problem. There's not a whole lot of energy in air. The issue with heating/cooling is the surface area.
With active heating/cooling, what really helps is better insulation. In Scandinavia and Germany people are insulating walls in new houses with 40 cm rockwool, or the equivalents thereof.
