Edit2: Note that X-COM (with hyphen) also uses a lot of randomness.
A definition under which X-COM is not a good game can only be wrong.
I'm generalizing of course, but there's a clear correlation between a game (PC or boardgame) using die-based outcome resolution and it being shit.
(...)
Also I'd like to point out that randomness is not the same as luck. A game can inject randomness in several ways that have varying degrees of luck associated with them; the ratio of randomness to luck varies with each implementation. The goal should be to achieve the level of randomness (and hence in a sense replayability) the designer is looking for while minimizing the control that luck has over the outcome of the game.
Luck that invalidates, precludes or replaces player choice/the consequences of player choices sucks (in a strategy game, obviously, not games of chance, etc.). The question isn't "how many times does the game roll the dice?"--it's "how much does that randomness actually determine the outcome of the game?" There are several acceptable--desireable--roles for randomness in a strategy game that I can list off the top of my head.
1. Randomness can inject greater challenge into single player games, forcing you to adapt to circumstances that are completely unforseeable and preventing any approach from being a sure thing.
2. Random rolls can abstract factors a game can't/doesn't simulate to provide an experience "truer to life" or at least the expectations of the player.
3. Probabilities allow more minute adjustments in statistics to matter and makes them more interesting. Even a relatively involved game that eschews probability has one fewer tool on its belt when differentiating between actions/items, e.g. all other factors being equal when taking a particular shot in an X-COM like game, weapons A & B will always hit and C will always miss and they deal 1, 2, and 3 points of damage, respectively, is less interesting than A: 100% for 0-2, B: 50% for 2 - 5, and C: 10% for 3 - 6, especially when it's very easy to reduce your options in the first scenario to a simple matrix of decision = outcome. Enough rolls mean that, yes, there's always a safest option and it'll be very similar to the options in the first scenario, but...
4. Low probability/high reward or high risk/high reward strategies are
fun.