It is also basically impossible to use a wheelchair while holding something in one hand, so if there's enough magic around to push a wheelchair, there's probably enough to make your legs work.

First, off the top, you can stop your wheelchair, use your hand(s) for something else, and then start moving again.

Second, you're making a lot of assumptions about the magic system. Every magic system has limitations. What if healing is a clerical spell, not a magic spell, and there are no clerics around? Maybe the nearest cleric who can heal is many miles away, perhaps over dangerous terrain inhabited by bandits, monsters, etc. Maybe the spell requires some very specific and difficult-to-obtain materials. Or maybe the spell is very high-level, requiring many years to learn, so clerics or mages charge a very high fee for this service. Any of these, or a combination, could be a reason why a disabled person (or a family member on their behalf) is questing.

Maybe the knowledge of the healing magic was held by some ancient civilization and it was lost when that civilization fell, but the disabled character has found a clue to where some ancient ruins could be unearthed where the secret might be found.

Or maybe the GM just says "Yeah, spells can't do that in this setting."