Rent is largely the exception to the modern rule. Most film adaptations have eschewed the broadway cast, generally citing either age or how famous the cast member is or is not.
Dreamgirls, Phantom, Les Miserables, Into the Woods, Chicago, Hairspray, Mamma Mia - these have all had new casts for film. Even stage productions like Proof have been recast due to "age" even though the time between stage and screen was 5 years.
Lion King has already been running for 20 years, and there is no reason to believe Aladdin won't have a substantial run.
I'd have loved an adaptation of AIDA, but even while Heather Headley was still on broadway, the rumors circulated about having Beyonce play the role in film.