Firtly, John died quickly enough that the civil war (John's supporters against those who wanted Louis on the throne) essentially fixed this problem, at least temporarily.

Secondly, Magna Carta demanded and condemned lots of things. It didn't do more than this- it was quickly repealed, and even when edited versions were confirmed, part of the problem was that Magna Carta couldn't be enforced. The 1215 document- the most radical- wanted 25 barons to whom the king would be answerable. This clause was removed in all reissues. Manga Carta was not enforceable. Arguably it became more so later, when the civil war was occasionally the alternative, but I'd suggest that Magna Carta itself was not enforced, and couldn't be.