I disagree completely. The fact that Amazon does not auto-focus to the search box annoys me greatly, since 99% of the time I find the items I'm looking for via search. Compared to Google, Youtube, etc. Amazon feels clunky.
Then why don't you just search via Google? "site:amazon.com bank of bob" or even most of the time you can just add the word amazon to your search query "amazon bank of bob" and I get exactly what I'm searching for.
To me you haven't made any case at all why others should have to suffer so you can have auto-focus on Amazon when your needs are already met elsewhere.
My favorite thing about DDG is that at this point there are so many bang syntaxes defined that if I don't know the syntax for something, I can often just guess and half the time I get it right!
"a foo" to search on amazon, "g foo" google, "i foo" imdb, "m foo" google maps, "w foo" wikipedia, "u foo" urbandictionary, etc... I have more but they are not public sites.
Chrome automatically recognizes searches on sites, so that you can just type "ama[TAB]" in de URL bar, and it will give you a site-specific search straight in the URL bar (provided that "ama" auto-completes to "amazon.com" for you, naturally). This works for basically every site you've ever visited that has search functionality. It's pretty decent.