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"I realize not everyone has an Apple Store nearby but many do."

That could be a handy additional service to offer, but they'd still have to provide a non-in-store method for all the people who don't, so it wouldn't be any more secure.

Facetime?

You need an Apple ID for FaceTime.

Whenever you do a password reset their is a possibility that it was performed by an attacker. However much you check their identity this will always be a risk. Therefore it makes sense for Apple to try and contact the user via several different methods. Call them on the phone, send a letter etc to inform them of the password reset. It must originate from apple, and be out of band. Having people go to the apple store does not achieve this.

If your solution to a technical problem is an Apple store, you have been drinking too much juice.