There is some debate in performance building circles as to whether or not you can add enough insulation below a concrete floor to eliminate the need for heating it. We have been on the fence about this and leaned to both sides at different times, but it seems we have now fallen off the fence, and landed on a warm floor.
Life is short they say, unless of course your feet are cold, then it will seem much longer. The floor of the Edelweiss House is insulated to R32, more than 3 times what is normally used in new builds. This seems extreme to some, but that is simply because floors are chronically under-insulated and any addition to that can be a foreign concept to lot of builders.
Having a heated floor is not an argument against greater insulation, it is actually the opposite. You wouldn't say "I don't need to insulate my roof much, because I'll be heating the air in my house".
Heating a floor increases the temperature differential between the concrete and the ground below it, which increases the rate of heat loss. Contrary to common beliefs, heat does not rise. Warm air rises, but heat goes everywhere. You need only pick up a hot coffee in a ceramic mug to answer this question for yourself. Does all the heat come out the top? Is it cold on the bottom? Absolutely not. Heat radiates from all sides, including the bottom. Your basement floor behaves the same way.
A heated floor will warm your feet and the air in the house (making it rise), but it will also be heating the ground below your house, and like any exterior surface of your home, the less insulation you add the more heat you will lose.
We have installed a radiant heat system with the intent of keeping the floor at a more comfortable temperature, but we rely on a small ductless heat pump (3 times more efficient on average) to heat the air. This may sound like redundancy, but these systems combined cost less to install than what you would spend for other full house high-efficiency heating systems.