I also prefer the roll of the dice. I suppose I ought to be careful as I have never played out a game in LL. I really enjoy the different directions that game often takes based on dice rolls. Every game can be a different game whereas in LL I can see the game tending to play out along predictable ways. That being said, re-rolls of early outrageous dice should be considered and I have allowed it and suggested it in my games when I was the beneficiary of the opponents bad dice. If I win, it’s not going to be because my opponent got diced early.
I think it adds to the game when you have to consider and plan for unlikely outcomes. It forces you to use more forces than you would like to and to hold some forces back for contingency plans. Everyone is a competent general and planner when the dice are going their way. The mark of a truly good tactician is the ability to build in flexibility to account for unlikely dice outcomes. If dice are always determining the outcomes of your game then maybe you ought to play a bit differently.