The 2x4s that have been sized this way do meet structural code. It was found that a full 2x4 is way over spec'd for what they were used for, so why bother wasting extra parts of the tree?
Pretty much everything built with dimensional lumber in the last century has been done with undersized 2x4s, and it's fine. The name stuck for historical reasons. Companies that build houses and order this stuff by the pallet all know what the real size is, and so do building inspectors.