Search Provider is not an extension it is just a setting in your browser so I am not buying the argument that is is for security purposes.

Also, these three steps are not intuitive i.e. you can't ask user to click a button on your website to initiate the change. While on Firefox, clicking on a button, a prompt gets shown to make your search engine default one. Even in case of Firefox, user has to explicitly click on check-box to make your search engine default.

Try here http://www.verticalset.com/