People preferring it and Apple or Mozilla asking Google to pay them to include the search bar are not exclusive.
If consumers prefer Google, and Apple couldn't make enough money with their own search engine to compensate for the lost users, it would make sense for Apple to pay Google for the right to use their search bar. Sure, Google could theoretically make money by giving it to them for free, or even by paying them to include it (see Mozilla), but why not get paid twice?
> and that Google doesn't make money on Android
I don't think anyone seriously believes that Android doesn't make money. Why else would Google put so much money into it in the first place?