I think the downside to split systems is being over stated here. I've never lived in a house with Central AC and don't notice any real difference in comfort between a house that has split systems and a house that has Central Air.
The House I was born in, had a 1970's era Carrier Split system, with a compressor the size of a large Fridge. In cooling mode the Fan continuously ran at the speed you selected and the compressor cycled on and off. Everything was always cool and comfortable, and due to its second vent (Hole through the wall behind it) it cooled a 4 bedroom house for over 30 years.
Every house since then has had more modern split system, and generally when the compressor stops, the blower fan slows to low, just to keep air moving past the thermostat. Its never humid or clammy inside, as long as the units are sized appropriately for the space they're cooling. If the units are undersized, then yes it stays very humid.
We live in a 3 story townhouse and prior to Christmas, we fully air-conditioned the Top level (Finally) with a 3 head single compressor Fujitsu unit. The upside for us, is we can now just cool two bedrooms (That are in use) are we can cool the entire floor. We couldn't find an installer that would do Central Air for the Top level as the Air return would've been at the top of 2 flights of stairs, and the system would've had to have been oversized for the rooms that needed cooling due to the hot air that would rise up the stair well. We had some pilot holes drilled in the floor to see if it would be possible to retrofit ducting to the main level, and short of Ending up with an obtrusive bulkhead or losing a chunk of Storage space, there was no way to get from the roof to the lower levels.
If you size them right, the Split systems work without issue.
Nathan