"Chatgpt, summarize this email into a few bullet points!"
Somehow, I doubt we'll notice. The reason we don't send the bullet points email today is that the receiver will think we're angry with them. In University the engineers all needed alcohol as a social lubricant, if chatgpt replaces it I expect we'll trade hangovers for higher electricity bills and carry on.
The sentiment will be no less fake. It'll just be better written.
Stripping that out might ironically reduce the need: Of people come to expect their messages to be automatically stripped of fluff, why include it in the first place?
The problem is that, exposed to enough writing that seems empathic but isn't, a person will learn that empathic writing is not sincere. We lose that as a society in the same way that if I check my email and see a "YOU'VE WON" subject I don't get excited, because I know it's fake.
Do we really want that? A world in which when you see an empathic message, the first thing you think of is that it's fake? I find the idea to be quite sad.
The converse could be true: maybe being inundated with fake empathy is almost as good as being inundated with the real thing, ala placebo effect (or the studies which have shown that just forcing yourself to smile can actually improve your mood).