"...does anyone open their browser and type in سرچانجن.com (or whatever) instead of typing the western script equivalent?"
Does anyone spend their life writing in those squiggly characters that just look weird to you? Yes they do. There's a whole world of foreign, squiggly-character writers out there, beyond your horizon. It was even there before the Latin alphabet existed. You just don't see it, because you live in your limited version of the internet with your limited character set. Get a life.