There are tons of effective QFTs that can be used very accurately to predict experiments below a certain (high) energy threshold, but which are not renormalizable. This is well understood. It means that the theory needs to be augmented to understand the higher energies, but does not at all mean the more fundamental (augmented) theory has to be radically different, such as classical. Everyone already agrees that the non-renormalizability of naive low-energy quantum gravity means something must be added.