Copywriter here (some of the time).
You know the old saw about how work can be good, quick, or cheap, but you can only pick two? AI is the definition of that in copywriting terms. It can do quick and cheap. It can't (in my view) do good. Yet.
All the AI-generated copy I've seen has been very... ploddy. It's grammatically correct, appropriately spelled and makes sense. But AI only seems to have one rhythm. It's dull to read. It can't seem to do wit, playfulness or that wilful bending of linguistic rules to create earworm wording.
Nevertheless, I've been slowly losing a segment of work to AI for about four years now. The sort of work I've been losing has tended to be the copy editing work — smoothing out Ts&Cs, policy wording, that kind of thing. Or writing functional stuff like nav for apps and websites, customer service comms and staff handbooks. Half-spammy social media posts that are more SEO and hashtags than meaningful content.
For some clients, who don't care if their site's modern slavery statement is crafted to within a gnat's fart of Hemingway, AI can do a 75% good enough job in a few seconds. Quick and cheap.
Overall, though, I'm not worried; more wary.
What AI can't do (for now, anyway) is pair up with an art director to toss around ideas for a campaign. It can't do jokes, plays-on-words or duality.
When AI writes the next VW 'Lemon' ad, I'll worry. Until then, nah.