Part of good stall maintenence in the US is stripping stalls to bare earth twice a year, spring and fall, and letting the floors air dry completely. I did this at the same time I powerwashed the barn for dust and cob webs. It was a great way to allow the floors to resettle and dry as well as controllng dust in the barn. You needed a solid of week of good weather to to do it properly though.
I was also a big beleiver in leaving the bedding pulled back from the wet spots while the horses were out, and rebedding right before they came in to allow maximum drying time, as well as using a lot of lime on the stalls to speed drying.
In a well run barn, it is not difficult to maintain clay or stone dust floors at all. In a barn were the muckers don't do a good job, or the stalls aren't done to the bottom each day, or the horses are in more than 12 - 14 hours a day, yes, then it does get messy, but that's would probably be the case no matter where you are.
I suspect if I had concrete floors like you describe, graded and with a drain, I would feel differently, but again, the only experience I had with them is converted dairy barns and it was an ongoing maintenence problem.
I am sure a lot of this does have to do with what you're used to and what's available and customary locally.
Now, how does everyone feel about barn aisle flooring? I greatly dislike concrete or asphalt (Macadam to our British friends, I think) because I've just seen too many shod horses skate on that footing. If I couldn't have mats or rubberized footing, I think I would prefer tamped bluestone or graveldust. Little more work to wet, rake and keep tidy, but easier on feet and legs and less risk of skating.