Biggs vouched for Luke's piloting skills. He's the best bush pilot in the outer rim territories you know! The scene was only partially restored to the SE, but it was addressed.

Rescuing the princess puts Luke in the good graces of the Rebellion as well.

I have no problem believing they might have been short a pilot or two. People do get sick at the worst possible times. Luke even said to Han they could use a good pilot like him.

IIRC, the radio adaptation added a scene where Luke trains in a simulator before the Death Star arrives?