For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option

https://devinjgpe949.iamarrows.com/why-many-older-salt-lake-city-homes-are-switching-to-ductless-cooling

For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option, especially where existing heating is radiant, hydronic, or space-heater based.