Does it harm a mattress to use it on a platform bed without a box spring?

It would be too high with a box spring, but some people say the mattress will wear out sooner without a box spring. Is that true? The platform bed has storage drawers underneath, and seems more useful than a box spring on a frame. Does anyone have experience with this situation?
We are building the platform with the storage, ourselves, because we couldn’t find one to buy!