The trouble is if they've been uploaded to literally anything other than a personal website, making such changes en masse would be either prohibitively difficult (DeviantArt) or outright impossible (X) depending on whether the site has a no-questions-asked image replacement option. We might see some of them start offering a built-in tool to apply the tag to selected pieces or one's entire gallery, but ironically the most anti-AI art site I know of is FurAffinity, whose owner would probably take 80 years to figure out how to code such a thing.
A better way to handle this would be to simply treat no-AI-allowed as the default, similar to how copyright law treats no-unauthorized-use as the default, and make artist incorporate a special tag into pieces they do want to let AI data farms scrape.