> 1) A proper, popular search engine is incredibly expensive to run. You can't do it for free. It's going to have to be ad-supported. But ads are the very opposite of Apple's brand.

They could also use ads, just in a more subtle and privacy friendly way like the search ads (https://searchads.apple.com/ or previously iAd: https://en.wikipedia.org/wiki/IAd) in the App store already.