Today, Apple is issuing an updated version of iOS 9.2.1 for users that update their iPhones via iTunes only. This update will restore phones ‘bricked’ or disabled by Error 53 and will prevent future iPhones that have had their home button (or the cable) replaced by third party repair centers from being disabled. Note that this is a patched version of iOS 9.2.1, previously issued, not a brand new version of iOS.
As I hoped, Apple has fixed iOS' behavior so that iPhones will no longer be bricked by Error 53. From the company's statement to TechCrunch:
We apologize for any inconvenience, this was designed to be a factory test and was not intended to affect customers. Customers who paid for an out-of-warranty replacement of their device based on this issue should contact AppleCare about a reimbursement.