I would suggest that if you want/need to machine wash the cross stitched item to stitch it directly on fabric. You can buy waste canvas to put over the fabric. I will also suggest if you are stitching on a knit type fabric to be careful not to overstretch the fabric. The very first t-shirt I cross stitched was of an Appaloosa, and it turned out to be a "family" horse, meaning the entire family could fit on its verrry looong back. :lol:
If you will only need to hand wash it, the aida will be great. It's not the stitching that will fail in the washing machine, it's the aida. It is just too loose to withstand the machine. I've been hand cross stitching for over 20 years now, and have never backed my fabric with anything. I have a customer that has had a hand cross stitched tote bag for over eight years now and it still looks great! I see her with it at the shows all the time.
(The pug on the bag in my avatar is hand cross stitched on aida-the ponies on the shirt were hand stitched directly on the shirt.) ;)