Sorry if this sounds kind of ignorant, but I do primarily backend stuff lol :)
Instead they have to have you the user do something to indicate which ones you can see and which ones you can't. That's why you HAVE to click on the squares. And if you click on white squares, it'll (wrongly) think you've visited sites you haven't. If you click on NONE of the squares, it'll think you haven't visited any of them, since it won't have any way to double check the info.
So that's why they can't "just render it outside the viewport." For sources, see the other comments by folks with good info.
It's cleverer than that. There are two positive controls (squares that are always black) and one negative control (always white). If you don't click both positive controls, or if you click the negative control, the page will tell you that you've failed the CAPTCHA.