This is giving me Black Mirror vibes. Like when that lady's consciousness got put into a teddy bear, and she only had two ways to express herself:
Monkey wants a hug
Monkey loves you
I get that you shouldn't go off on customer service reps (the reason you're angry is never their fault), but filtering out the emotion/intonation in your voice is a bridge too far.
Most of the time angry customers don't even understand what they're angry at. They'll 180 in a heartbeat if the agent can identify the actual issue. I agree, this is unnecessary.
I did phones in a different century, so I don't know whether this would fly today. But, my go-to for someone like this was "ok, I think I see the problem here. Shall we go ahead and fix it or do you need to do more yelling first?"
I can't remember that line ever not shutting them down instantly. I never took it personally, whatever they had going on they were never angry at me personally.
Then again, I do remember firing a couple of customers ("we don't want your business any more etc") after I later became a manager and people were abusive to staff. So you could be right, also.
In college, I worked at a call center for one of the worst Banks of America (oops, meant banks in America 😉). Can confirm that, and I dealt with a LOT of angry customers.