The theme and title sequence to Fresh Prince of Bel-Air quickly became an iconic part of the show. However, when you watch it in the context of the show's later success it's painfully obvious that it was almost certainly shot on a shoestring budget for the pilot episode. Several of the shots consist of cheap graffitied backdrops and stand-in extras. Many of the details contradict plot points from the finished show.
For instance, Will's mother in the intro...
...looks completely different to his mother in the show...
Have the show's producers ever talked about this? Did they want to keep the original title sequence for consistency or because they thought the cheap production values were endearing - or for some other reason?