I wonder why Apple is not starting it's own search engine. I mean yes, they get >$1Bn per year making Google the default on iOS+macOS, but they have plenty of cash so they wouldn't need it. They would get immediately ~10% market share when it is launched, just because it would be made the default on their devices. From their they just need to present better search results than Google (which shouldn't be that hard right now) and can only grow further.
As another commenter here said "Google does not make money by helping you find what you are searching, it makes money by keeping you searching". That only works when there is no competition. But once Apple would be in the game, people would use what presents them with the better results. Right now, I don't feel there is real competition.
It's legally not anti-competitive behavior (as in, both Google and Apple's lawyers believe so) because it's just a 'default search engine' fee - everyone knows that iOS/Safari is the most lucrative platform to be the default search provider for, so a large number like $20 billion is to-be-expected. I'm sure that, in a lawsuit, Apple would argue "if someone else came and paid us $21 billion, we'd take it and drop Google/start a yearly auction" but no other search engine has that budget.
Apple is surely free to make their own search engine, and to an extent, they do - in Safari, the "suggested sites" feature is a search engine but one that only returns {single result | no result} and only works on iOS/Safari. On that same note, you can prove this by tracking search engine user agents for your website to look for Applebot/0.1 hits (if your site is popular enough).
But what would be their incentive to do so? Normally they launch products and make it exclusive to their devices so more people will buy iPhones, but that is difficult to do with a search engine. Otherwise they would have to get into the ad business like Google.
Apple is a publicly traded company, and every company needs to grow into new markets to make more revenue. And they also maintain their own browser Safari, even though on macOS they could just withdraw from market and leave the field to Chrome and Firefox. Even amongst macOS users Safari usage is very low and doesn't make Apple any money.
On the other hand you can see how Google is using its dominance in Search to push its browser and mobile OS - once you login to Google in Chrome on your phone, suddenly they can track you when you use their mobile Apps etc. And Apple is trying hard to grow in the "Services" field, i.e. through Apple Music and Apple TV - both available to Windows and Android users too. Just as they made a buttload of money with iTunes and the iPod because they also targeted Windows users.
Running a search engine is a massive money sink, regardless of its popularity. It's the surrounding ad network which makes money. Competing with Google and Facebook in that regard is an impossible battle, and something Apple has already failed at a couple times now. They have since pivoted into creating a privacy friendly image, so emulating Google simply does not make sense for them.
As another commenter here said "Google does not make money by helping you find what you are searching, it makes money by keeping you searching". That only works when there is no competition. But once Apple would be in the game, people would use what presents them with the better results. Right now, I don't feel there is real competition.