I associate The Rockford Files so completely with James Garner's charm and the vibe of 70s California, I can't imagine anyone doing well in a modern remake. And I've not observed David displaying that much charm in recent decades (though he's certainly the celebrity with the strongest physical resemblance to Garner). Maybe they should have aimed a little lower, like a remake of Spencer: For Hire.
I suppose the answering machine thing could be voicemails on a phone Rockford is always forgetting to check. But you know whatever modern interpretation of the theme song they do is going to be vastly inferior.