I don't remember if setting search via click had ever been done, but certainly when I was a kid (10-12 years ago), I vaguely remember when I visited sites like Yahoo, there would be an underlined text that read "click here to set this to be your homepage!"

I don't remember if it was actually possible without user to confirm or not, but I supposed the security reason prevents that from happening today.

The closest thing I can see is bookmarklet which is also very dangerous.