Flooring materials are irrelevant from an energy-efficiency standpoint?
Flooring materials aren't usually thick enough to prevent heat flow. They do not replace floor insulation.
energy efficiency vs. Comfort
We all appreciate the "warmth" of carpet. But we should not confuse it with energy efficiency.
We feel carpet warmer than stone, even if the carpet and the stone flooring are at same room temperature - something that depends on the direction of heat flow (between the flooring and our skin), which in turn depends on the conductivity and thermal properties of the materials.
Anyway, though not important from an energy efficiency standpoint, the type of floor covering is important in some cooling and heating strategies, or for radiant floor heating purposes.
In the case of radiant floor heating, the floor covering should not interfere with the heat transfer, which makes carpet, cork or even wood flooring "bad" choices, contrary to ceramic tile or stone…
Many people complain about their floors. They are unconfortable. They are cold.
But the problem is not in the floor coverings, or in the type of floor. The problem is often lack of insulation of the basement/crawlspace walls and floor; or has to do with lack of under-floor insulation.
Wood, bamboo, cork and linoleum flooring have a better insulation value than stone, ceramic and other types of tile flooring. And that can help control thermal gain and loss and make them advantageous in some heating and cooling strategies. They do not replace under-floor insulation, but they can help keep the floor and the house more comfortable. On the other hand, materials like stone and tile flooring are good at storing heat (from the sun or other sources) and do not block energy flow, which is important in strategies involving passive solar strategies.