This is not true. You can only push if you roll as many successes in the attack as there are successes in the defense. Then the attack is considered to have failed but you can push back the opponent.
I play this game since shadespire, the first season. I too had the feeling that the warbands were not balanced, but after a while I learned that you need to play following a tactical plan. And that plan should fit with the nature of the fighters and should be supported by the proper cards. Otherwise, the game indeed feels like "you are doing stuff but I doesn't lead to anything'. So, you move, you attack, sometimes you score, sometimes you don't. In the end you count your points and then there is a winner. If you have a tactical plan and you can execute it, then it really feels like winning!! Or like somebody said: "I love it when a plan comes together".
As far as the dice are concerned: know that you should play 3 games. When you execute your plan better then your opponent, you'll win 90% of the time.There can be a loose in those 3 games because you're opponent gets lucky on a crucial moment in the game, but normally it won't happen 3 times. Also, remember that in tournaments: you need different plans against different warbands... So your warband also needs to be versatile...
Keep playing and keep finetuning your deck, you'll love when your plan comes together.
P