Sibling comments are completely correct. Graphics simulations often require quasirandom sequences; the particular sequence is not important, but any correlations in the sequence will be visible in the output as artifacts, so we want a decorrelated sequence.
If this is not enough of a real-world example for you, then Monte Carlo methods also show up in weather modeling, financial planning, and election forecasting. In those predictive systems, there is extreme uncertainty and dependence on initial conditions, which we model with quasirandom sequences and seed numbers respectively. By running many simulations with different random sequences and then examining all of the results statistically, we can get good estimates of future behavior.
Edit: Oh, you're not in good faith. Okay, cool story. Best of luck with whatever imaginary idea of "unpredictability" you're trying to define, but you might want to return to actual maths at some point.