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

https://dantewmio857.urbanvellum.com/posts/how-to-cool-a-salt-lake-city-home-that-has-no-ductwork-2

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.