It's a design constraint rather than a fundamental truth
It's not inherently "true" so much as a design constraint when constructing descriptions of microstates.
For example, consider a description of microstates in which it is true that all of them are equally probable. Then, redefine the ensemble such that it's exactly the same, except half of the original microstates are now described as a single microstate that encompasses all of them. Obviously, they're not equally probable anymore.
For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge.
can be restated as:
When you're constructing a description for your ensemble of microstates, try to define them such that they're all equally likely.
Such physical models don't tend to require perfection, so it's not like everything'll instantly break if there's a small error in the description of microstates where some are a bit more probable than others.
I mean, sure, we try to fit our models to reality as best-as-possible, but some error's gonna happen.
For example, folks often talk about ensembles of coins that can be Heads-or-Tails. The obvious microstate description for a bunch of such coins is where each microstate corresponds to one set of Heads-or-Tails value for each coin. But even if we select that description, which sounds fair enough, coins don't tend to be perfectly fair, so the description won't be perfect.
A real-life scientific example of that is with chemical isotopes. This is, it's possible to ignore the differences between isotopes of the same element; this introduces some error, but in common practice it's generally allowed as a reasonable approximation unless there's some compelling reason not to.
Basically, the trick's to select microstates that're approximately equally likely. The better the fit, the more logically consistent the arguments based on it would tend to be.
Entropy tends to grow due to degeneracy
Statistical Mechanics is all about how degenerate states are more likely.
For example, an ideal gas is said to evenly disperse about a room because there're many more microstates in which it is rather than, say, all of the gas particles being smooshed together in some corner of the room.
This isn't that any single dispersed microstate is more likely, but rather there're way more dispersed microstates than non-dispersed microstates. This is:
Each dispersed microstate should still be as likely as any other microstate.
However, there're astronomically more dispersed microstates, such that they're collectively more likely than the collection of their alternatives.
However, say that you redefine the set of all states in which gas particles are dispersed about the room to be a single microstate. Then, yes, that one micro-state would be far more likely than any other. The fundamental postulate of Statistical Mechanics simply recommends that you don't define them that way, since the heterogeneity of it screws with other descriptions.