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.
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.