Alphabet is an ad company that depends on collecting vast amounts of data. Search alone does not make money.
What do you mean? Search generates more money than the rest of Google together. Through ads, yes, but Google search could run ads even without the rest of Google. Nothing else Google does generates nearly as much ROI as search, just that they can't invest more into search since they already got the entire market there so they do other things like putting countless hours into optimizing those search ads.
google search is so personalized now, you only get best in class search if you log out first.