No, but SD is an even more unique case. Even though "San Diego" is covered by both Center and Approach, everyone seems to live using JANAPs without complaint. It didn't always used to be that way, as the Navy helos used to file with their tail codes, and sometimes you'd hear a jet with their code. But now, whether it be through additional MOUs and/or institutional inertia, everyone seems to just use their JANAP and ATC doesn't complain.
JAX has slowly become that way now too, which is why you'll hear even the VP birds use their callsign rather than their LIMA code (except for -30).