Do stochastic models have any merit at all?

I studied stochastic processes at university and mathematically they are a cool topic. However, I highly doubt they're ever gonna be even remotely relevant to real life applications. All attempts to model the stock market so far failed miserably. And as the Monty Hall problem shows, the right choice of probability distribution is highly dependent on subjective knowledge / information. So it's basically impossible to find the right model for a given situation. In particular if you're dealing with an event which cannot be repeated then the predictive value of stochastics is basically worthless since stochastics only applies to experiments which can be reproduced infinitely in order to determine whether their outcomes follow a certain distribution.