I think it's always safe to take paper copies just in case of computer malfunctions. Saves arguments and stress. Some places want the vouchers others do not but why take the risk for a couple of pence of paper and ink?

I also print the flight confirmation because sometimes BAH don't credit the avios on the holiday and I need to remind myself about them until they get posted. Once the itinerary is complete you can't get it off MMB.