Rebuilding statistics will not help if the cause of the bad plan is something that the cost based optimizer is not even trying to model.

Stored procedures in this context are just a clumsy workaround to control the planner so your comment about API layer is irrelevant. But if you like, you can write stored procedures in a ton of different languages. And if you do not have source control for your database artifacts, you are doing it wrong. A common reason for stored procedures is to not have a bunch network roundtrips in the middle of your transaction logic while you are holding onto locks / have an open conflict window.