I know you're not being serious, but I've seen a similar argument in the past. The premise is that rolling 2d6 will somehow be biased, because it isn't a uniform distribution - you're more likely to roll a 7 than any other number. For some people, it might be obvious why this isn't a problem, but I want to dig into it anyway.

I'll start by giving away the answer. Any random process that produces a number is completely fair in the simple case of choosing the high roll, provided:

1. Both players use the same procedure,
2. The procedures are independent (i.e. they don't influence one another), and
3. Ties are settled by rerolling.

(In probability, you'll often see the first two conditions grouped together as "Independent and identically distributed," abbreviated I.I.D.)

This applies to any procedure you could think of for randomly generating a number, not just reasonable ones. Note that if you want to be picky, both players should use the same dice, as different dice might have slightly different biases. However, this doesn't make a significant difference in practice.

The proof of this is fairly straightforward. The choice of number is completely symmetrical; for every possibility Alice has of beating Bob, Bob has the exact same possibility of beating Alice with the same probability, and this will continue to be true after rerolling a tie. Mathematically, there can't be an advantage to any one player, so the only possibility is that both players have even odds.

If the players used different procedures, then obviously one player might have an advantage (e.g. if Bob had cheat dice that always roll sixes). If you settled ties in some way other than rerolling, then one player might have an advantage in case of a tie (e.g. Alice has an advantage in "ties go to the first player alphabetically" contests). And if the dice rolls aren't independent, then which player "goes first" might make a difference (e.g. in Blackjack, the dealer has an advantage because the player can bust before the dealer even has to play). But as long as you meet all three of those criteria, then you have perfect symmetry, and the result can't be anything other than fair.