We use renormalization arguments (and experiments) to change the couplings of a theory and suppress the higher energy physics (saying things like “whatever the fundamental theory, this will be true of the low energy theory.”). And we then get some set of fields, correlation functions, etc. My question is just about the possibility of, say, a theory of quantum gravity that compromises the renormalization arguments we’d been using to determine the sensitivity of EFTs to the space of possible high energy theories. So, perhaps the actual theory wasn’t included in the high energy theory space?
Physics theories model experimental data. Starting from the very successful Maxwell equations solutions, which model macroscopic electromagnetic behavior, the the solutions of Schrodinger's equation which clarified the spectra of atoms, to the good fit of the present standard model of particle physics to almost all data accumulated from the 1960s, physical theories are an encapsulation of a great lot of measurements, if the are successful. They are successful if they can predict new measurements correctly. If they are not falsified, they are considered validated and standard.
Thus , if a possible higher energy theory for quantum gravity does not embed the lower energy effective field theories, it might be a competing theory for gravity, but not for a theory of everything, in effect it will be a different effective theory.
A theory of everything headed by quantum gravity should embed all the validated by data effective field theories, otherwise it is falsified as a theory of everything.
The data trumps mathematics. Of course it might mean that nature has not given us a theory of everything