The point of Monte-Carlo method is that you can tradeoff accuracy for speed. The longer you run your algorithm the more accurate you get.
But what's even more interesting is that we can often use the contrapositive : You can get shitty accurate result real fast.
Instead of exploring all paths, you explore only one path picked at random.
And that's where it shines : when you put it into the most imbricated loop of your algorithm.
For example when you want to learn a neural network which autoroute. Typically you would have the outerloop which is updating the neural network parameter, and the inner-loop which is computing a path through the graph.
When you use Monte-Carlo this inner-loop which control accuracy can be reduced to 1 iteration if everything is bias-less, you will have a slower outerloop due to higher variance but the machine learning should """theoretically""" learn.
This is what allows you to build policies which intuitively always pick the right decision. Like in chess or go, you have some monte-carlo tree search variant like alpha-go-zero or alpha-chess-zero or alpha-router-zero, where even without the search part, the giant cache (encoded by the neural network parameters), once trained, can compute your best guess path in one pass through your neural network aka constant time (with a constant which can easily trade memory for speed by augmenting the number of parameters or training for longer).