Part of that is the Rebellion we see on the show is split into cells rather than grouped together as a single fleet. It's not that there aren't Y-Wings or X-Wings out there, it's that Commander Sato's crew runs A-Wings.
Except the A-Wing wasn't even designed until after the battle of Yavin! One more thing Disney apparently retcon'd without even realizing it.
While it's newer material, seeing as the Jedi starfighter looks like a precursor to the A-Wing, I'd be surprised if that was the case. And it's not a change that really effects anything.