Consider a magnet with temperature $T$. We can observe its net magnetization $M$, so we say that a value of $M$ specifies a macrostate. Statistical mechanics tells us which macrostate the magnet is in. To do this, we compute the free energy $F(M)$ and minimize it. The free energy is defined by $$F = U - TS$$ and hence depends on the entropy $S$. This entropy is determined by the number of microstates that could be compatible with the given macrostate, i.e. the number of spin states that lead to the magnetization we observe.
This procedure has always felt sketchy to me because it seems to rely on some subjective notion of knowledge. The reason that there are many allowed microstates is because we've postulated that we know nothing about the system besides the net magnetization; if we did know something else, it would decrease the number of consistent microstates and change the entropy, which changes $F$.
As such, it looks like the result of the calculation depends on the set of macrostates we use! For example, suppose I somehow attached a measuring device to every single spin. Then in principle, I could specify my macrostates with a long list containing the state of every spin; then there is only one microstate corresponding to each macrostate. In this case, $S = 0$ for each macrostate, $F = U$, and the minimum free energy is attained for minimum $U$.
Then I conclude that the system is always in the ground state!
What's wrong with this reasoning? Is it somehow illegal to make this macrostate choice? Could acquiring all of this information about the spins necessarily change how the magnet behaves, e.g. from something like Landauer's principle? In general, can changing macrostate choice ever change the predictions of statistical mechanics?