There may well be some writing jobs that are safe for the reasons given in this post, but that doesn't help all the writers I know who have already lost their jobs and are struggling to find work.
It's not enough that humans can tell the difference and feel an ick, there also need to be enough organizations willing to pay money for that difference. From my vantage point, there are not. It turns out that for a ton of the writing produced by companies, the quality of the prose wasn't really "load-bearing" as Claude puts it. That writing is there to occupy a space and look professional at a glance, the same way elevator music is tolerable for the duration of an elevator ride.