The search term persistence is nice, when you want to change what you searched for, e.g. add another word to narrow it down more. It’s been the behavior on mobile for a while, and I was skeptical at first, too, but you just really don’t need to see the URL of your search engine. Well, unless you’re trying to add it to the browser, but at that point, the search term persistence won’t yet happen.
Yeah, sometimes I even then can’t download the picture, even though I was looking at it just then, because the server can apparently tell the difference and returns an error code instead.