Banishing Light and similar effects are fine because they're dealing with permanents. What happens when permanents show up on the battlefield is already figured out in the rules. Non-auras are just there, auras get attached to another thing, things trigger if they need to trigger, and everything is happy.
There aren't really rules right now for a spell just showing up on the stack, which is what would happen if you say "target spell is exiled until X leaves the battlefield". When a spell gets put on the stack you need to figure more stuff out like what modes are picked, what targets are chosen if any, additional costs paid, etc. A spell just showing up from exile won't remember these things, because it is a new object from the original spell that was cast.
The two main ways things end up on the stack currently are either casting it, which involves choosing all those things, or copying it, which copies all those choices from the original spell. So it makes sense to have this spell get cast, since that handles it all.