Did he?
Looking over an early version of the script, it seems that there’s nothing to indicate that Luke did not bury or burn Beru and Owen’s remains.
The scene where he sees their bodies ends thus:
LUKE: Uncle Owen! Aunt Beru! Uncle Owen!
Luke stumbles around in a daze looking for his aunt and uncle. Suddenly he comes upon their smoldering remains. He is stunned, and cannot speak. Hate replaces fear and a new resolve comes over him.
After that, we switch to Darth Vader, and then back to Obi-Wan burning the Jawas. Then, next thing you know, they’re going to Mos Eisley. Watching A New Hope confirms this. The novelization follows the same order: Luke despairs, switch to Vader and Leia, switch back to Obi-Wan burning the jawas, There is no proof that Luke did not deal with their bodies in the interim.
That said, if he really didn’t deal with their bodies, there’s a plausible reason. From the novelization:
“Damn your Force!” Luke snarled with sudden violence. Now he turned and glared at Kenobi. There was a set to his jaw that belonged on a much older face.
“I’ll take you to the spaceport at Mos Eisley, Ben. I want to go with you—to Alderaan. There’s nothing left for me here now.”
It may have been that once they were dead, he felt no further attachment to their bodies. Note that Obi-Wan’s concern for ceremony is described as “archaic”:
Working together, the two droids helped Kenobi throw the last of the bodies onto the blazing pyre, then stood back and watched the dead continue to burn. Not that the desert scavengers wouldn’t have been equally efficient in picking the burned-out sandcrawler clean of flesh, but Kenobi retained values most modern men would have deemed archaic. He would consign no one to the bone-gnawers and gravel-maggots, not even a filthy jawa.
He might also have been unable to retrieve their bodies, as discussed in another answer.another answer.
Now, in Legends, Luke did leave them behind, and buried their bodies after the Battle of Yavin, as detailed in the comic Star Wars 7. But in canon, he did not necessarily just leave them lying around.