Another question that one can ask is "although we have framework theories to play the role of metamodels?"; and indeed we do have. The obvious question would be: "Why not use first order logic or high order logic or category theory or set theory as computation of frameworks"?
Well, this can be done, and in fact it has been done. And indeed such systems have been utilised and we have formal tools called precisely with the same names. We have the system FOL the system HOL, and the system SETL, which indeed try precisely to play the role of meta-frameworks, of meta-logical, of metamodels.
But if we are going to indeed use such system, such abroad generality, we will bring about yet more opaque encodings. It appears in a metamodel to be convenient to focus on some pervasive concept in computation, that becomes some specific feature to that metamodel. And especially if you want to keep an high at building interactive tools, it is important to be able to have these sorts of pervasive concepts, to have in the foreground. And so these systems like first order logic, high order logic set theory, are indeed a little bit too general.