Well, skill is a factor, but I dont care how good you are, If I get perfect UKR rolls as Russia, and then Germany gets creamed trying to take it back, Im gonna win as Allies 9/10 (taking into account future crazy rolls)
I personally wouldnt be any more likely to make a risky move knowing I had a mulligan (unless this mulligan was only limited to the first turn), knowing that I only have one reroll, and that the second round results may be even worse. And if the rolls are then awesome, your opponent could choose to reroll those rolls.
Personally, I just hate knowing the eventual outcome of a game with ~90% certaintly after the first turn in some games, when I would suggest there is the least amount of skill (most people have only a few preset opening moves, with slight adjustments for previous battle results). Not to say EVERYONE does good first round moves, but skill is reflected in moves that develop over multiple turns.
Skill is not determined by the results of 3 ARM 3 INF 1 RTL 2 FTR vs UKR, though often games are.
My two cents!