Not an expert, but isn't most classical music like that? Most long pieces (e.g., concertos?) start with the main theme that gets unpacked in later parts of the performance.
Though I feel very bad writing ^^^. The rest of those pieces are very worth listening to. I listen more often to the first movement of the Ninth.
Is it by design? Was the composer aware that a certain part would end up being that one exceptionally popular one?
The probabiliy that a part not at the beginning is (becomes) popular is higher than for the part at the beginning, because there's more parts not at the beginning than the one at the beginning.