Building a good search engine is expensive. Perhaps not as expensive as AI build out.
Market share is currently Google (91%), Bing (4%), Yandex (<2%), Baidu (<1%), Brave (<1%)
Google can and do already monetize automated search from AI models.
Heck, if they wanted to, Google could turn off search and make you go through their AI model to get information.
Imagine that. That's how powerful they are.