The Michelson–Morley experiment was indeed very important, but it has not proved in any way the non-existence of ether. It has just proved that the ether does not behave as it was previously supposed, i.e. like the materials with which humans are familiar.
It does not matter at all what names are used for it, one may choose to name it "ether", "vacuum", "electromagnetic field", "force field" or anything else, but all the modern physics, since James Clerk Maxwell and William Thomson, is built on the assumption that the space is not empty, but it is completely filled with something that mediates all the interactions between things.
Only before the middle of the 19th century, the dominant theories of physics assumed the existence of true vacuum. The existence of true vacuum is possible only in the theories based on action at a distance, like the Newtonian theory of gravity or the electromagnetic theory of Wilhelm Eduard Weber, but not in field-based theories, like the electromagnetic theory of Maxwell or the gravitational theory of Einstein.
It is rather shameful for physics that the main result of the Michelson-Morley experiment has been the replacement of the word "ether" by "vacuum", as if a change of name would change the thing to which the name is applied, instead of focusing on a better understanding of the properties of the thing for which the name is used.