Fundamentally, Google protects its search by owning all entry points to it (or paying massive fees for competition-prohibitive distribution deals.
The strategy can be seen at play with the Chrome browser, Android and its licensing model for hardware manufacturers, paying Firefox and Apple for placing search as default in their respective platforms. They know that once distribution barriers for search fall, their existence is threatened, explaining even moves like Google Fiber.
We wrote at length about this issue in our blog https://0x65.dev/blog/2019-12-22/google-competition-is-just-...
Google is not a search company, it is an ad company.
An ad company needs data about you. A search company needs data about web sites.
Owning Andriod assures that they get the data about you.
The rest is irrelevant.
That, and extending the scope of search: with mobile their search (and in particular their map search) is far more relevant to brick and mortar advertisers than desktop search alone could ever be. That's a huge market and on top of it on mobile a search user is less picky with the result/suggestion/ad continuum because of the constrained UI. And while most desktop searches are entirely unrelated to monetary transactions and those that are tend to be about spending less or getting more, many mobile searches come quite close to "where can I spend my money". This is where you want to be as an ad medium. The end-game for this is voice UI while driving, where the search provider can basically send physical traffic to the highest bidder.