Yes, it is true that this thread has not taken the "Why Quantum" essay to heart. But the stated intent of the essay seems to be somewhat different from what you describe. All the essay seems to propose is that entropy might show why the microscopic universe follows quantum logic instead of a host of other possible models.
Frankly, the essay asks why the universe is the way that it is, which is actually one of those questions that have no answer...at least no unique answers. This question appears most often in the context of religion or philosophy and so I was quite surprised to find it funded as a "Foundational Question."
Actually, I have been a little disappointed that the FXQi website does not actually ever seem to recognize the nature of some foundational questions that really do not have answers. There are foundational questions that people have been asking for tens of thousands of years and that have no answers. First and foremost is the question:
"Why is the universe the way that it is?"
Religion and philosophy address this question endlessly and the result is always more discourse about the answer, not a single testable answer.
I use entropy quite a lot in my work with solution thermodynamics and am always disappointed when the first definition of entropy is not the logarithm of the total number of states of the system. If the system has one state, its entropy is zero because the logarithm of one is zero.
It is very true that the entropy of an isolated system must increase over time, and yet the entropy of many systems, i.e. galaxies, within the universe have decreased significantly over time. Since the number of possible states of a system always increases over time, entropy always increases over time. However, there are no truly isolated systems in the universe and so the laws of thermodynamics are highly scale dependent.
The entropy of quantum action is quite well behaved, while the entropy of gravity action can be quite peculiar. Trying to use entropy, which is the way the universe is, to explain why the microscopic universe is the way that it is, i.e. quantum, seems circular.
The universe is the way it is because that is the way it is...