It's only when you begin to care, copywriting becomes a pain.
Getting in and out of a hundred shoes can be exhausting.

You start to miss 9-5, phone calls, dental appointments, and your grandma's 83rd birthday, cracking a headline that checks all the boxes.
You begin to lose sleep, friends, hair, and your mind, trying to find a hidden French lion inside a blank notebook.

Somewhere between the metamorphosis of a brief becoming the final artwork, you feel a part of you dies.
The anti-ageing cream ad you're writing grows you a new wrinkle. The irony!

That said, if you've ever worked closely with good copywriters, you'd find that they always care.
Care for the brief, the insight, the campaign plan, the design, the media budget, the client, and their customers.

Apart from craft and story-telling, see if the copywriter you’re looking at gives a damn.
And if they tell you that they do, then don’t take their word for it. Instead, look at their work. Chances are that it will show.