Our rink does something similar to this for kids during public sessions, but at one of the ends rather than the center. It doesn't stop the icefreestylers from messing around in there.....
France is slowly updating its rinks. The older ones are terribly sad. Louviers ( a town in Western France, Normandy),and Angers are the most recent to get an update, with new rinks that just opened this September. The calibre of the update, as far as I can tell, is directly related to the calibre of the local hockey team. Angers is getting a really nice complex. Louviers, while I'm sure it's nice, is not getting the same. My city's was updated about 15 years ago. We have a single slab, and stadium seating on one side of the ice (we have a mediocre, but well loved, hockey team). 2 slabs, like they're doing these days, would have been appreciated, and well used here. I bet the newer rinks anywhere in the Alps are fantastic.
I would have been surprised if they'd have let you skate on anything other than a public session. All sports require a license and insurance in case of injuries goes through that. Plus all lessons are group lessons, so they wouldn't have known what to do with you. I suspect it would have been the same in Italy.
Nice that you're doing some rink tourism!