As an appraiser in the rural midwestern states I see these very often in home additions, conversions, and outbuildings.
As an owner/user of a Fujitsu Halycyon mini-split heating and cooling system I can say they work when used properly. My electricity bill using the mini-split system is much less compared to the ceiling cable heat and window units that were installed when I bought the home. Also, it provides much better cooling than window units. The heating from ceiling cable "feels " better and functions properly at temperatures below 20 fahrenheit. The heating performance from the mini-split during below 20 fahrenheit is not sufficient.
When I purchased my home it had ceiling cable heat and did not have central air conditioning. Only window units and a window unit installed in the wall of the living room. A few years later I was annoyed by the inconsistent cooling and noise of the window air conditioning units.
I got 3 estimates for a central forced warm air heating and cooling system and 3 estimates for mini-split heating and cooling. The 3 FWA estimates were $12,000 or more. The 3 mini-split estimates were $6,000 to $12,000.
I had a 24 seer mini-split unit installed with 3 interior ductless units. The advantage is there is no need to install ductwork, it is fairly quite, easy to maintain, and each interior unit is controlled individually by remote. The disadvantage is unless there are interior units in every room the doors need to remain open to provide heating and cooling.
From my experience used as main heating and cooling for the home, mini-split is better than no central heating and cooling, but inferior to central heating and cooling.
Mini-splits are best used as a supplemental source of heating and cooling in an addition or outbuilding, unless it is installed in every room of the home