It seems to me that inappropriate activation of a stick shaker can be used to identify an AOA malfunction on the affected side of a 737, even if you are not equipped with AOA compare capability.
Any pilot worth his salt should know when he is in a potential high AOA situation, and when he is not. If you are straight and level at 250 knots or above, you should not be experiencing a stick shaker.
How well are AOA system failures handled in emergency procedures?
Continuing a flight with a continuous stick shaker makes it likely that a subsequent actual need for stick shaker may not be reacted to if triggered on the opposite side. However, the crew of the preceding Lion Air flight did not disable the stick shaker.
Disabling the stabilizer electric trim and staying out of RVSM airspace seems to have been the limit of their cockpit procedures.