Keep in mind that considering IVs, Natures and all that faff, you might end up spending more time preparing for the game than actually playing it. Also, all the random opponents you'll encounter throughout the game will yield equally random EVs, so unless you do one of the following your team will be nowhere near competitive in the end:
1) EV train your Pokémon beforehand, or at the earliest opportunity. Unless you do this in Super Training (which takes hours, especially if you're going to do it for the entire team), your team will be massively overlevelled before you even get off to the start.
2) Reset your EVs and EV train them in the middle of your adventure. This also creates a rather long and uninspiring break, besides your team will not be competitive until the very end (which might go against the spirit of your challenge).
At any rate, such a tailored team will bulldoze through most situations the game cares to throw at you. Using only the strongest Pokémon around will severely blunt any resemblance of a challenge. The journey is (usually) what matters, and what you're doing will take most of the spontanity and uncertainity out of it. Beating in-game opponents, be it regular trainers, evil teams or Gym Leaders will mostly be a routine business, and since your team is predetermined, you'll get to make few choices while playing.
I'm not saying that you shouldn't go through with this, I'm just warning you that it might be more fun to plan the playthrough than to play it. There's a reason why the usual OI stance on competitiveness is: "Just mess around and complete in-game at your own pace first, then acquire competitive Pokémon after you've finished the story".