Before diving into the nitty-gritty of search engines, I'd like to introduce a simple metaphor that summarizes the main point of this guide.
Google is a football. It's easy to grip, is great for long passes, and can be kicked. It does its job well.
But if you use it to play baseball, you're going to be disappointed. Try to dribble a football down a basketball court, you'll get plenty of laughs, but few points. And it should be obvious that you're not going to make par on the golf course with a ball twice as wide as the holes.
You see, in the world of libraries and information, there are lots of types of content. Each works differently from the others and has its own specialized search engine. Each is its own ball game, and each uses its own type of ball.
When you ask for a single search box to cover all content, you're asking for a single ball that will work for all sports. Sure, you can design a medium-sized ball that will kind of work for most games. Maybe some kind of cross between a volleyball and a soccer ball. It would work reasonably well for those sports. And you could kind of play football, basketball, or softball with it, though not well. But tennis, pool, or golf? Probably not.
Basically, there's no physical way to make a ball that can be used to play all games. For the same reasons, you can't design a single search engine that will work for everything. And the more generic you make your ball/search engine, the less useful it's going to be for specific games/searches.
So the next time you ask, "why don't they have one search box?", imagine playing ping pong with a bowling ball. That's why.