Recently I was able to play a game of Spirit Island remotely and for the sake of time we decided that we would only fish Major Powers out of our respective power decks whenever someone else got one, and we were fine with the possibility of people having the same minor powers. How much does this affect the game?
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This should have very little effect, especially if you included the expansion power cards.
There are a few edge cases - eg, in a 4p game, 2-3 players getting Elemental Boon can result in players being able to hit high-level innates much earlier than usual, which depending on Spirits (*cough*Serpent*cough*) might distort things to some degree. Beyond those, pretty minimal. (And not getting to the point where you reshuffle the Minor Power deck is actually true to the original vision of the game - the ideal is never being guaranteed that a given Power Card will come up.)