Even though the main DID spec 'expects' JSON, you are already implicitly constructing that document for single-key OP_RETURN DIDs (as do other specs like did:key); so you could use CBOR or bencode or some other more space-efficient (and ∴ cheaper) encoding than "just" ASCII JSON in an inscription/envelope?
Perhaps the spec should also specify UTF-8 encoding even though that's what everyone would guess