While I agree that Meloetta going mixed probably isn't the best idea, Relic Song isn't exactly a "free" turn. It's a 75 BP STAB attack, and when Meloetta-A uses it, it's coming off of a base 128 stat. Oh, and it has a 20% chance to put something to sleep.
And, in the situation you mentioned, Meloetta-P can just hit Gyarados with Thunder without changing forme, since even uninvested with a neutral nature, it OHKOs the Sub+DD set after Stealth Rock. The real problems that set has are priority moves and generic walls/bulky Pokeon who aren't weak to either of its moves (Gliscor, Celebi, Landorus-T, Volcarona, and even Metagross, since it has the special bulk to comfortably take a Meloetta-P Thunder). Oh, and Thundurus-T, who isn't even a wall.
Generally, Meloetta should be trying to smash face from either the special side or the physical side, since it doesn't have the coverage to really pull off both (thanks to having to take up a moveslot with Relic Song...Normal typing isn't so good). I'd say its biggest problems are bulky steels who aren't weak to Fighting (Scizor, Metagross, Jirachi), who can take hits from either side well enough, since Meloetta doesn't have a hugely powerful Fire move. Unfortunately for Meloetta, those are really common.