Little variable-speed units sold as ductless minisplits are fairly inexpensive in the US. They’re especially reasonable if you actually use them in a ductless configuration, because you don’t have to install ducts.

The fact that they might have a higher list price than a conventional single-speed outdoor unit and indoor evaporator coil is a red herring, as the conventional units can’t do anything on their own, and they need a furnace and a fan added to be useful.