At the house I have mentioned we installed mini splits. There are six units since we have multiple rooms. The setup has worked well because we selected units with sensors that detect when a person has left the room. The units spin down to a efficient setting and after a period of time turn off. Rooms like bedrooms are off during the day but will be occupied during the hottest part of the day sometimes. These are all inverter units as well.
They're a good retrofit for a house with no ductwork and for which you don't want to install any.
But I would not choose to have a bunch of minisplits (or even a multi-zone minisplit) over a central air system in a tight well-insulated house for the following reasons:
1)They don't have very good filters, and they seem to clog quickly, causing the minisplit to error out. My central air unit has a media filter that is Merv 8 rated, 25x20x4, and I can go over a year before I need to change it.
2)They have no provision for bringing outside air into the house. My central air unit has an Aprilaire fresh air intake system that has a duct to an intake on the side of the house, a damper, a fan, and a control that selects the amount of fresh air per hour in 5 minute increments. I currently have it set at 20, this keeps the radon level in my house as measured by an Airthings Corentium below 1 pCi/L. (This is "build tight and ventilate right" in action).
3)Sometimes I run the central air fan to circulate air through the house, especially in summer. This brings some of the cooler air from the basement upstairs. Can't do that with minisplits. (And my central air fan is an ECM so it runs at a low energy-saving speed in fan-only mode).
4)My central air system is zoned, I have two thermostats, one for upstairs, one for downstairs, both connected to an Aprilaire zone controller with dampers. I just have one air handler which handles both zones.