I guess that I have trouble imagining how any law of physics that I know of would enforce such a rule. The whole point of statmech is that the 2nd law is an emergent phenomenon: it's not a separate influence on the universe independent of the known fundamental forces, but rather a consequence of how those known laws play out in cases with many particles and/or states. What you're suggesting is some additional influence at microscopic scales, and that seems quite implausible to me. (Just how strict are you imagining this rule would be? If two states had phase space volumes in a 51/49 ratio, are you suggesting that the system would always pick the 51?)
It's hard to list intuitive counterexamples to your suggestion here, since anything intuitive is by definition part of a macroscopic system that would obey the 2nd law anyway. But... for instance, are you saying that you don't believe in the Maxwell speed distribution in an ideal gas? If no molecular interaction could ever take a system from a larger to a smaller total phase space, then every molecule in an ideal gas should eventually converge to the RMS speed. That's a clear experimental prediction, and I'm pretty sure that the usual answer has been well-tested (both explicitly and implicitly).
It's hard to list intuitive counterexamples to your suggestion here, since anything intuitive is by definition part of a macroscopic system that would obey the 2nd law anyway. But... for instance, are you saying that you don't believe in the Maxwell speed distribution in an ideal gas? If no molecular interaction could ever take a system from a larger to a smaller total phase space, then every molecule in an ideal gas should eventually converge to the RMS speed. That's a clear experimental prediction, and I'm pretty sure that the usual answer has been well-tested (both explicitly and implicitly).