Hi there! We have rebooked as well and saved a lot of money. I don't think it will be different for the European season, so I expect to know our room very last minute. I think the reason why they assign last minute is to keep availability in many categories open for late bookings.
They are actually marketing the Dream here in Europe (we live in Germany) quite a bit and I can see Europeans booking very late to go on the cruise, Americans less so because of the long flight.
Doesn't keep me from checking daily in the app if it shows a stateroom!