And as we know, "free" search is really just a way to sell ads. So Apple would be effectively getting into the ads business and competing with google on that front. I hope I speak for other Apple users when I say we don't want that. I pay the Apple tax to have some of my privacy respected and a less ad-riddled OS.
Apple could theoretically use search as a way to compel people to buy Apple devices, or to become iCloud subscribers, or whatever. It doesn't have to be an advertising business. That is a manoeuvre they are quite familiar with.
In reality, I'm not sure Apple could actually create a search engine that is compelling enough against the competition to see people drawn into the Apple ecosystem, but in theory...