Should you purify your Shadow Pokémon
As with any question regarding overall strategy and collection in Pokémon GO, the answer will be unique per player. However, we can present you with some tips and tricks as well as a lot of information on how Shadow Pokémon works in the game, allowing you to make the best choice possible. In short, if you are a competitive gamer or someone who wishes to have the rarer versions of all Pokémon in the game, keeping them in their Shadow form is probably the best bet for you.
Why? Because Shadow Pokémon in Pokémon GO get a significant attack bonus for staying in this state. While canonically keeping a Shadow Pokemon is a bit bad, they got it after being tortured and pushed to their limits by Team GO Rocket, the game has a clear incentive to keep them that way. It's that way because a Shadow character receives a 1,2x bonus to all their attacks, which exceeds any advantage you get from having high IVs over your opponent.
Conversely, when you purify the Pokemon, they will lose this bonus in favor of cheaper power-up costs for Stardust and Candy. So of course, if you have little of it and you need to strengthen a character, then purifying may be wise, but this is a temporary situation and there is no turning back. Some quests require you to purify a number of Pokémon, so you can find non-competitive characters like Rattatta and Zubat to take care of those. For Mewtwo, Moltres, Mudkip, Machop, or other useful Pokémon however, trading is almost never worth it.
But another thing to note is that any Shadow Pokémon will have Furstration, an unnecessary move, as a charge attack. There are ways to deal with this though, so be sure to do them before you launch your Shadow Mewtwo into battle. Otherwise, the answer to whether you purify your Ghost Pokémon in Pokémon GO is usually 'no', although you could disagree if you're not ultra competitive.
