Can't think of a reason good enough for ME to do what you are suggesting. I'd run 4 tires of the same make, same model, same size and the same amount of rubber on the tire. I might feel differently if I had a new set of tires and ran a nail through the sidewall of one with only 1000 miles on it. That would be about the only exception I can think of.
You may get by with what you're considering just fine, but think of the number of $$$'s that could be involved should a drivetrain problem develop. Idiot lights and computers are there to protect you, and they might, but what if they don't? Play silly games, win silly prizes.
Then again, do it report back and the rest of us will be able to give a solid answer next time someone asks.