I think there are two ways randomness* can work well (and enhance the need for skill) in games:
1) random results that you have to respond to by adjusting your strategy. (E.g., many card games, where you use skill to make the most of the hand you're dealt.)
2) having to account for probabilities of random results in your strategy, before they occur. (E.g., backgammon, where you try maximize the chance of having a good move regardless of how the dice turn up.)
There's a third way, which we agree is a fun killer: randomness that disregards or substitutes for strategy, so you either don't make any decisions or your decisions don't matter. (E.g., Candy Land, chutes and ladders, War, or most other games for very young children.)
*I think "luck" is not quite the same. Dice and cards are random; luck is whether or not that randomness works out for you.