Don't think the problem is with the amount of indexed pages. Just the way we need to access what we already know and use. Chrome provides us with the top 8 most frequent sites. This keeps us going again and again to the same sites. Harder to make a habit around a new site.
1. Windows desktop or smartphone usually show 50-100 application 2. Google search has to show billions of web pages
therefore I argue that it is simple impossible for Google to show billion of pages like Windows desktop and smartphone. Hence Google show the search box instead of icons.