Palkia doesn't 100% need support, it simply needs support for one of it's sets. While it's most dangerous set needs rain support, which Kyogre does by simply going into the battle, it's like it doesn't even need support. Rain themed teams may need the rain, but the rain comes into play permanently on turn 1. This means there is always support, so all rain team pokes function to their ability 100%.
Even so, something like specs Palkia can take advantage of both the rain and sunlight, which either weather will appear in ubers (Sandstream teams just get ripped apart by STAB surf anyways). Draco Meteor pummels anything in it's path, and with specs backing it, almost everything dies miserably; including Mewtwo.
Also, just to prove my point, here's an example of how Palkia beats Mewtwo. Specs Draco Meteor from a Modest Palkia OHKO's Mewtwo, even with max sp. def (nuetral nature) and minimum HP. If he runs EVs into max sp. def, he loses out of speed, meaning he has to split his EVs into HP, Sp. atk, AND speed, meaning he loses out on even a 2HKO. Palkia then proceeds to 2HKO.
Now, if Mewtwo runs max HP but no sp. def EVs, he's still OHKO'd by Draco Meteor. If he runs max HP and Sp. def (enhancing nature), he's 2HKO'd by Spacial Rend/Surf (with or without rain), while he can't even manage a 2HKO himself. Basically, no matter which way you put it, Palkia OHKO's Mewtwo before Palkia gets 2HKO'd, or 2HKO's Mewtwo before he can be 3HKO'd.
If you want proof, use a damage calculator. I ran all the correct numbers.