Private
I can just imagine the trouble we'd be able to cause if there were magical creatures everywhere.
The Sorting Hat has changed, then. It should realise that without the houses it wouldn't even have a purpose. And it'd be horribly impractical. What would they do, have everyone together? Think of how long the dormitories would need to be.
You'll make sure that Mr Barton doesn't get hurt though, won't you? Muggles are rather fragile.
Asking too many questions is a fault of mine, I'm told.