In Legends continuity, A-Wing were designed and fielded after the Battle of Yavin, which is why you don't see them before Endor. Disney did a semi-retcon by having them show up in Rebels around 5 years before their former conception.
About them being the "newer" craft, you are comparing oranges to apple, though. What's the better vehicle : a motorcycle, a sedan or a pickup truck? If you want raw speed and maneuverability, the motorcycle is probably your best bet. For a slight drop in maximum speed, though, you could be a lot safer in a sedan, and be able to bring some friends with you. The pickup truck would be slower, but would also allow you to bring a lot more stuff than the other options would. While a motorcycle could be the best option to commute to work on a daily basis, it really wouldn't be my go-to pick if a friend asked me to help him move out of his house.
In Star Wars, it was pretty much the same thing with the A-, X- and Y-Wings. The A-Wings were meant as a counter to the TIE Interceptors, which were a lot faster and better armed than the common TIE Fighters. To achieve similar performances, the A-Wing sacrificed shields and durability, but was also heavily modifiable to suit specific needs. The A-Wing was a huge feat of engineering (at least in the SW Legends), as it managed to be just as fast and well armed as an Interceptor, while still having some shield capacity. The Interceptor had four laser cannons to the A-Wing's two, but the A-Wing had access to concussion missiles, specifically designed to take down enemy starfighters.
X-Wings, on the other hand, were meant to be the "regular" superiority fighters, able to take a heavy beating before going down, usually taking down a few TIEs themselves before doing so. Being much larger, the X-Wing also had access to the very versatile proton torpedo launchers, which could be used for dogfighting, bombing runs or capital ship assaults. The Y-Wings, in the mean time, were intended as slower bombers, with larger payloads but limited dogfight capabilities. Another result of the "Galactic Arms Race", in a fashion similar to the A-Wing, was the creation of the B-Wing, originally intended as a replacement of the Y-Wing. With even heavier shields and targeting capabilities rivaling those of smaller capital ships, they were meant to attack capital ships, using their strong defensive capabilities to live through their bombing runs.
In the end, the A-Wings were not meant to be the "better" or "newer" craft, they were intended as a specific counter measures for TIE Interceptors, which only became apparently superior to X-Wings when their speed and firepower allowed them to make hit-and-run passes at Alliance pilots without them being able to catch up and fight back. The Alliance needed a fighter fast enough to force the Empire into a proper fight, but sturdy enough to live through it, and the A-Wing was born.