The use of inverter drives in appliances now is based mostly on increasing energy efficiency. In centrifugal machines, like pumps, fans and some types of compressors (scroll), the energy used by the motor varies at the CUBE of the speed change. So if you can slow a motor down to 1/2 speed, the motor consumes 1/8th of the energy. In a refrigeration system, the amount of refrigerant being circulated has to to with the necessary cooling at any given moment. Without an inverter drive, i.e. the compressor is at a fixed full speed, if you needed less cooling, you had a valve that throttles the coolant, but the motor still goes full tilt boogie. The energy consumed DOES reduce because of the lower flow through the valve, but not as much as if you were to eliminate the valve and slow the motor down instead to reduce the flow. So the longer you can run art reduced speed, the more energy you save compared to an older designed system. This is now being done in refrigerators, washing machines, even new heat-pump based dryers.
In addition, using an inverter means that you use a 3 phase motor, even though the source is single phase, because the inverter just uses the line source as a "raw material" to create DC that then gets "inverted" back to pseudo AC. The motor runs more smoothly, lasts longer (there is no more centrifugal switch or capacitors in the motor) and is quieter than a single phase motor. Yes, the motor must be specially designed to run on an inverter drive, but for an OEM making millions of mini-splits per year, that's irrelevant.