I think the explanation of entropy's blind spot is a bit off. It's not actually a problem for entropy if something is generated by a rule, you can calculate entropy for things like the continuous fractions for instance, with an easy rule to generate them for any particular number. Likewise for decimal expansions.

The real blind spot is that entropy is meaningless for a specific sequence, you can't really ask about the entropy of pi if you don't have a theory for how the numbers are generated. Sure if it is pick a uniformly random real number between 0 and 10 then both files have equivalent entropy, but sending pi is also vanishingly unlikely.

There's actually a more subtle way in which this is a blind spot, which takes a bit more machinery. You can define entropy for an ergodic system, which could be considered a kind of mathematical RNG. Now as it turns out this provides a way to generate something almost equivalent to a particular distribution except that this argument only holds for most starting points not all. A direct example would be how pi generates a perfectly fine random distribution of digits (we think) but something like 1/3 does not.