I doubt that the same number of people willingly choose Google, otherwise they wouldn't be paying so much money to be the default. That's a lot of money to throw away.
Outsourcing arrangements many different motivations, it’s not just money. Otherwise, basically any outsourcing arrangement can be said to be “throwing away money” for one party.
Nobody "chooses" anything, that's the point. If you want to stop using Google on stock iOS, you have to opt-out. Same goes for Android, it's not a market share thing so much as it is an abuse of ubiquity. Defaults are powerful, and a competitor that lets you buy out their defaults is apparently powerful enough to prevent competition.
Google deserves the scrutiny here, but this whole situation really illustrates how hopelessly America is headed towards an antitrust reckoning. FAANG has gone rogue, and foreign regulators have been sounding the alarm for years. The only remaining question is if the FTC has the stomach to butcher their finest pigs.
For everyone with Windows, you start off with Edge/IE and then Bing as a default search engine. Yet, most switch to Chrome + Google almost instantly. People care about their browsing experience more than we give them credit for. Remember in 2009-10 when Chrome was new, it managed to win market share cos of superior product when it was not the default on Windows/Linux/MacOSX. On mobile too, the behavior is likely going to be there to a certain degree. While Google pays Apple a massive fee, there was an admission earlier in the trial that both Mozilla and Apple would still go ahead w Google (even without the deals) because of superior UX. Not sure if both said it, but one of them certainly did.
[1] https://danariely.com/the-power-of-defaults-in-how-we-eat/
You could innovate and make a better product and it doesn't matter because you can't outbid Google.