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.