Which websites are shown in the search results is not influenced by whether Google has ads on them.

The only thing that influences Google search results is Google's desire to keep as many people using Search as often as possible, since nearly all of Google's money comes from showing those text ads at the top of the Search results. This is all public information, you can read it in the 10K etc.

So if Search sucks, it's not because Google has the wrong incentives but because they can't solve the problems Search faces.