I have a large soft holdall and a small one, both have a flat side., so there shouldn't be a problem. Dubai airport aren't saying you have to use rigid cases just those with one flat side, I have seen people checking in kit bags but not every time I fly. So I see just a very small amount of travellers will have to change their luggage if using Dubai airport.
I think the major problem at the baggage handling is the oversized irregular shaped packages like some of those in the picture.
My local airport has regular flights to Eastern European airports and foreign workers use these flights to travel home for visits and I've see all sorts of shapes of packages being checked in, same thing in some middle eastern airports where foreign workers are travelling back to their home countries.