I was a victim of this fallacy before, and I guess when humans are faced with dire events, they will always devise something to help get their minds at ease. The Monte Carlo fallacy is no different to that, as it's just a way of the human brain to 'cope' with unfortunate events giving them a false glimmer of hope that everything will be fine. No wonder people are losing tons of money to gambling; they give in to these instincts and let these overwhelm them over reason and logic.
Truth is humans are way less logical and reasonable as they may like to believe, and it is easy to guess why, have you ever sit down to consider every single possibility that may happen due to your actions? And do you do this for every single thing you do? Hardly, if ever.
We simply do not have the time to do this, as often most of the decisions we take have to be taken in a matter of seconds, so we tend to go with our instinct on most situations, and while most of the time this is the right approach, there are instances in which this is a bad idea, and this fallacy is one of those instances.