In the Disney version of Aladdin, is not the father we see, but the absence of the father that is significant. The movie doesn’t tell us what happened to Aladdin’s father, only the results of not having one. A line during one of the early songs is telling: “I’d blame parents, except he hasn’t gone ‘em.”
Without them, Aladdin has been reduced to a “street rat”, moving from place to place, stealing just to eat, and having a terrible reputation.
Luckily, the movie shows that there was more to Aladdin than his street rat identity, that he was a “diamond in the rough.” He was able to overcome his circumstances and become someone worthy to marry a princess.
You can easily see however, how the story might turned out very differently. He could have easily ended up with a permanent jail cell or even before the executioners ax. The effects of not having a good stable father in his life were profound and obvious to all who knew him.