I was just coming here to say exactly this. You could also use a partial index (that is, an index with a WHERE clause; so, "WHERE json_field LIKE '%foo.bar = baz%'" or whatever).

you can, but in order to build a partial index, the function needs to be immutable. not exactly ideal in this case.

Immutability is perfectly appropriate for that use-case, though. Creating an index via a function that may return different outputs when provided the same input is always going to lose.