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Ran both a Tyrantrum and a Flygon on my team on my first run. Any ice types I swapped into Delphox and both outsped every dragon type that I dealt with anyway for a decisive OHKO. Fairies again I used Delphox to defend against, since Delphox might as well be as Anti-Fairy.
The game's stupid easy as is, so I don't think anyone should worry about running same types on their team unless they try to go competitive and use a non-mono/weather team