are X-Wings capable of FTL travel for no reason?

Heh, that's actually the canon reason. Whereas TIE Fighters would launch from star destroyers like aircraft from a carrier, X-Wings would jump into hyperspace along with the frigates they were escorting.

The X-Wing is explicitly hyperdrive equipped. That's also part of why it has an astromech droid seat in it (R2), apparently so the droid can handle the jump calculations. A lot of later technobabble in the expanded universe expounded on this after the fact, but I presume this decision was made on a snap basis specifically so Luke could go to Dagobah in his cool ~~plane~~ spaceship.

You get to make hyperspace jumps yourself in your X-Wing a few times, fittingly, in the X-Wing games.

Star Wars had basically no concept of fuel until like, one of the recent movies I didn't watch. Obi-Wan calls a TIE fighter "a short range fighter" in A New Hope. Luke flies an X-Wing all over creation; several are shown jumping to hyperdrive alongside other larger ships in Jedi, it's established that X-Wings are FTL capable.

Back when they made the first movie they literally used WW2 fighter footage to design the final battle with the Death Star.