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I love and hate this new feature. There should be an option to choose to EV train strictly through Super Trainer or the old fashioned way. If you want to properly EV train you can not use that Pokemon in battle period because it tracks both battles and Super Training, which can be a major pain in the ass.
Everytime I get a Pokemon that I feel I'll use the whole game I have to stop everything for an hour to Super Train it up since I can't battle with it otherwise. Major pacebreaker.