In my opinion playing good has a much bigger inpact in winning a game than luck.
For example:
It is an even game so far. Your mage is more early game and your opponent is more lategame. Despite that you start to focus damage on his familiar. You need 3-4 rounds to kill his familar, with good/average rolls you would have only needed 2-3. Now of course you can blame bad rolls for losing the game, but from an authorial point of view the strategy to focus on the familiar was the mistake, not the bad rolls. They only made it a bit worse.
Of couse I won't deny, that at least average rolls are important and constantly rolling below average can mess up even a good strategy. But taking risks is a part of Mage wars, easy example:
Your plan is to cast a wall and then jet stream the opponent through the wall. And behind the wall there are 2 big hitters waiting to damage the enemy mage further. Big hitters: 5 dice each. Wall: 5*2 dice. Jet stream: 2 dice
I have at least 3 times observed this situation. And you can already guess what happened. Effect die below 4. So no push. = ~15 dice dmg less this turn.
Why? Because the caster was greedy. Forcepush would have been 2 mana more expensive but because he wanted to make 2 dice more dmg and save 2 mana, he risked it.. And it backfired.
Now you can say: well, it was bad luck and that is the reason he lost in the end.
Or you can say, the decision to use jet stream was wrong/a calcualted risk.
I hope I could make my point. I don't think that Mage Wars has too much randomness in it. It has to some degree, yes, but you always need to take it into account when deciding.
/edit: I would like your idea a bit changed. To make sure not to mess up very important rolls where theoretically you have a very high chance of succeeding: Expected dmg -2
So if you have 3 rolls and you only need 1 dmg to kill a creature (without armor), you don't have to roll, because you can use this rule to solve it. Same thing when you have a 5 dice attack and the enemy creature has 3 life left(no armor again). 100% sure destruction.
But always demanding to have at least average rolls is a bit too demaning.