Depending on how much precision you'd like for your answer, Monte Carlo methods can converge unbearably slowly, since the standard deviation is proportional to 1/sqrt(N) as you add more samples. I recall once having to run 100 billion simulations to get the mean of a certain quantity to within a few decimal places. I'd take an infinite series over that ant day of the week (well, as long as it's not something as slow as the Leibniz series for pi/4).
Of course, such precision relative to the standard deviation is rarely necessary for most practical situations.
As a friend in grad school used to say... "An infinitely long Monte Carlo simulation recapitulates the underlying probability distribution perfectly, but we don't want to wait that long.":
Yeah, it’s the practicality. Most business decisions don’t need more than three sigfig [source?]. We only tend to think about precision on things that already have it.
Unless you are trying to prove the existence of a subatomic particle, I am not sure what business decisions have anything close to that level of certainty.
Kinda depends on what you mean by "business decisions". Repetition can bring in a high need for confidence. You don't want to have your life depend on a piece of equipment that has a one in a million chance of failure if it gets tested a thousand times an hour. Pricing things can also need a lot of certainty, like in HFT. But most things aren't either of those cases and people are commonly off by an order of magnitude.
Of course, such precision relative to the standard deviation is rarely necessary for most practical situations.