Zippable covers make washing your mattress cover a breeze. Just unzip it and toss it in the wash. When it's clean and dry, zip it back around your mattress. This can help allergy sufferers keep their mattress covers free of allergens.
However, a zippable cover is not a replacement for a mattress protector. Mattress covers are permeable. That means even zippable covers still let allergens seep into the mattress itself. Washing a zippered cover won't get the allergens out of your mattress's comfort layer.
Mattress protectors, on the other hand, are impermeable. They don't let liquids or particles through to your mattress. So when you wash them, everything comes out. That's why you need a protector, even if you have a mattress with a zippered cover.