Mathematics as a lingua franca is useful and I believe you are correct; ultimately, I suspect all mathematically based systems _will_ be mappable to each other if they are sufficiently comprehensive.
The only flaw I really see is its closed Universe. Platonic. Timeless. Eternal. Not really a ‘flaw’ per se but the map remains a map, even if a highly detailed one with great power of prediction. It’ll still have the gap.
The block view of Spacetime won’t have any trouble with it.. because it too is a mathematically based conceptualization. but other views of Time and experience may.
Then again, the map *is* the territory ultimately for we utilize the map as we navigate the territory. Even without a map, we simply write the map in our minds as we go along. Still a map, still navigating territory, both combined, superimposed, even if not expressed in any language but the internal pattern making processes in the brain.