The problem is that your linked peltier consumes 22.8W of power to pump those 10W. That is a horrible efficiency, and completely useless for most applications.

The problem is that your linked peltier consumes 22.8W of power to pump those 10W. That is a horrible efficiency, and completely useless for most applications. At that point you're probably better off with plain old resistive elements when trying to heat, or literally anything else if you are trying to cool. Being limited to a small temperature difference and power capacity per area isn't that big of a deal when you stuff a whole bunch of them together, especially considering the goal is to replace traditional building-sized heat pumps. Needing tens of thousands of them only matters due to cost - and that's way less of an issue when it is more efficient than the alternatives.