The approximation of VNM rationality is foundational to most of economics. The whole field is basically “hey, what happens if you stick together VNM agents with different utility functions, information and resource baskets?“. So pretty much any successful prediction of economics is an example of humans approximating VNM-rational behavior. This includes really basic things like “prices increase when supply is expected to decrease”. If people lacked (approximate) utility functions, then prices wouldn’t increase (we’d just trade things in circles). If people weren’t taking the expectation of that utility function, then the mere expectation of shortage wouldn’t increase prices.
This is the sort of thing you need VNM utility for: it’s the underlying reason for lots of simple, everyday things. People pursue goals, despite having imperfect information about their environment—that’s VNM utility at work. Yes, people violate the math in many corner cases, but this is remarkable precisely because people do approximate VNM pretty well most of the time. Violations of transitivity, for instance, require fairly unusual conditions.
As for the risk of mugging, there are situations where you will definitely be money-pumped for violating VNM—think Wall Street or Vegas. In those situations, it’s either really cheap to money-pump someone (Wall Street), or lots of people are violating VNM (Vegas). In most day-to-day life, it’s not worth the effort to go hunting for people with inconsistent preferences or poor probability skills. Even if you found someone, they’d catch onto your money-pumping pretty quick, at which point they’d update to better approximate VNM rationality. Since it’s not profitable, people don’t usually do it. But as Wall Street and Vegas suggest, if a supply of VNM irrationality can be exploited with reasonable payoff-to-effort, people will exploit it.