Why does it take several weeks to get into Amazon?

Yesterday, I published my new book at Lulu,com, where they print the book when someone orders it. This is the way to go and the only reason it has not happened more is that the printing industry is holding back, making it cheaper to print a few hundred or even a thousand copies than one book. If you are in the mass distribution industry, like a publishing house usually is, this means slightly cheaper cost per book. If you do not count the fulfillment, the storage, the dead trees which will have to be thrown away, and so on. Even the most conservative publishing houses have moved to making their books available as e-books after the book stopped selling. Which is an artefact of the way they market books, by the way. There is no reason a book could not continue to sell forever.
So in that perspective, it is a bit strange that a book takes several weeks to appear in Amazon, or Google Books. If you deliver a PDF, they do not have to scan it. It can be read automatically. Unless they have to check it manually, there is no reason for a book not to appear instantly. And if they trust the publisher, that should be the case.
Now, I have to wait four to six weeks to see if the book sells on Amazon. Well, let's wait. I will prepare the next phase of my publishing idea in the meantime....