I don’t think they would have called it Bing. It would get the DarkSky treatment.
Apple has far more of a network of users than Bing. They don’t need Bing’s users or brand.
“Bing” would be the default search on iOS and macOS and it would instantly have an order of magnitude more users than Bing.
I’m not exaggerating. There are over a billion active iPhone users. There are 100 million active Bing users.