The MLB should just ban check-the-check. Baseball already has too many swinging strikeouts where batters actually swing. Plus, it would cut down the length of games if batteries couldn't appeal every single time a hitter flutters an eyelash. At least make it like with replays; each team is limited to three check-the-checks, so pick your spots.
The home plate ump's job is to call balls and strikes, while base umps call plays on the bases. We never see the home blue overrule a tag or slide call at third base, even when he has a better angle than the base ump (for example, standing behind a sliding runner; that's a personal peeve from amateur leagues, where there are only two umps).