Login window's search behavior change

Hi,
Is it possible to have "not-hidden" search field in the login screen above new site list view?
as such, search the domains/ips in the search field and only results displayed instead of tab thru large list. and an X as a clear search button at the end of the search field.
thanks
haluk yildirim

Thanks for your suggestion.
We will see, if more people ask for this.