I think you’re making my point for me, a diacritic instead of an h to indicate a sound change would be more efficient and reduce ambiguity.

The problem is that not only is there no central authority for spelling reform in English, the cost of replacing the existing body of work would be too large, even for changes that would be more consequential.

My argument was never that my proposal should replace the current system, just that if you did want spelling reform, it would make more sense than the thorn.