Maybe it could work in a smaller home, which doesn't have a basement, and where people didn't care about looking at all those ugly head units. In general, minisplits are too small, too ugly, and all require individual drains, so not really a good choice for whole-house cooling in a larger home. Also, dehumidifiers generally reside in basements around here, and not many people are pumping AC into their basement, if only for eastern-PA's generally-high radon levels, alone.
In my case, I'm only using two minisplit systems to cool two very small spaces (1400 sf + 260 sf) that are isolated from the rest of the house. The main part of the house is cooled by two very large traditionally-ducted Carrier AC units, something like 10 tons total. I presently have two dehumidifiers plumbed up with auto drains in the basement, and since my boiler runs all summer (hot water) that keeps the third "wing" of the basement dry.
edit: I guess the radon comment probably didn't make much sense, and could be something to favor mini-splits. Around here, people generally don't pump traditional ducted AC to their basement, even when they have a finished basement, because basement radon levels in our part of the state are often at or above the treatment threshold (4.0 ppm). But a minisplit exchanges no air with the rest of the living space, making them ideal for cooling a finished basement, if you can deal with the drainage so close to grade.
