So I guess at that point "wait time" just becomes a vanity metric? Or to show their clients "we only make callers wait X amount of time compared to our competitors"?
There's the old adage that as soon as a metric becomes a goal it ceases to be a good metric because it starts to be gamed. It's probably not universally true but it shows up again and again in things like NYC's COMPSTAT program where a decent idea becomes a goal without measuring the right thing and you wind up with police just harassing people because you've gotta get the number of arrests up or you'll look bad at the next COMPSTAT review.