Literally the two stupidest, most irritating things that bad websites do

It depends. If I type something into the box, will it search with a “site:” or something similar, or will it simply do a Google search over the entire internet? Or, is there an option? If there is an option, don’t make “The Web” the default because I wanted to search the whole web, I wouldn’t do it through your site, I’d just use Google directly. Using Google to allow people to search within your site makes sense. Basically just embedding Google within your site does not.