If they just built their own search engine and used it as default, and it provided high quality un-manipulated results, I think even more would flock to Apple. Yes they'd take a (big) hit up front by losing out on all of that free Google money (estimated to be ~$12B in 2019), but then they could actually say with a straight face they were truly privacy advocates and won't sell their users data to Google via the Google Search Engine.
Saying how privacy conscious a company is, while literally making billions of dollars by indirectly selling a lot of their customers data, really rings hollow with me. Build a search engine. It's not as hard as building Apple Maps, and will do more good in many ways. Hell, even non-Apple people might use Apple search and fall in love with the results, bringing them into the Apple fold.