I'm really not sure what you are talking about. Go to you.com and type a search query. No need to make anything the default. No need to install an extension.
Edit: Ah, now I see. It's because I'm a Safari user. If you go to you.com in Safari it works fine. However, if you go to it in Chrome it does indeed work as you described, asking you to install the extension and whatnot. My mistake.
It says on the front page "Add you.com to Chrome to get started" which to my mind implies that in order to get started you have to be using Chrome and add the extension to it.
You don't have to, you can just use it as a web page, the text is misleading and should be changed.
I think that's only if you're using Chrome. I'm in firefox and just did some searches like you'd do on any other search engine. That's a really weird design choice regardless.
Edit: Ah, now I see. It's because I'm a Safari user. If you go to you.com in Safari it works fine. However, if you go to it in Chrome it does indeed work as you described, asking you to install the extension and whatnot. My mistake.