The kind of user who likes to browse will probably browse using a mouse, not a keyboard like us nerds. So the position of the cursor doesn't matter to them.
I hardly ever go to Amazon and not directly search for something (except maybe during Black Friday deals when I just click on the banner). I'd bet Amazon loses money by making me do an extra mouse click into the search box every time.
Unless there's a sizeable proportion of users who go to the homepage and scroll using the keyboard, I don't get it.
Also, if you're a nerd, just search right in the browser. If I want to search Amazon I never actually go Amazon first I just type "a", hit tab and then my search terms. Chrome is smart enough to do the rest and I get right to the SERP on Amazon.
edit: Mouse movement = tracking content with eyes? http://news.ycombinator.com/item?id=5333496
Why do you think they obsess over dropdown menus?