I received different answers from a number of locksmiths. The Repair or Replace predicament was there was no definitive reason for the cause of the broken tailpiece. The majority of locksmiths chose to replace the deadbolt lock. A few would replace the lock cylinder and some would replace the broken tailpiece.
The reasons were divided. The locksmiths who chose to replace the tailpiece or the lock cylinder believed that if the problem re-occurred, the customer would call them back. They would discuss the situation. The less expensive tailpiece replacement may not be solution versus lock replacement, the more expensive solution. Some said they would leave the choice to the customer.
The locksmiths who chose to replace the lock believed that if there was a problem, replacing a part may or may not be the long term solution. They did not want to take the risk of an unhappy customer as your reputation is always at risk if the repair does not last. It is harder to get a new customer, than to keep an existing customer.
Although lock replacement is more expensive than part replacement, for them it was the best solution. One locksmith felt that if there was a problem with a more expensive piece of door hardware like an exit device, then maybe they would consider repair.
Finally, although no one likes to talk about making money, replacing the lock will provide a significantly greater profit than replacing a tailpiece for about the same amount of time.