I think Apple would've seen the name Bing and being associated with it as being a net negative for brand reputation.
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.
Apple hasn't released daily active users for any of it's services, but it has argued recently that iMessage has less than 45 million active users in the EU (https://9to5mac.com/2023/09/04/imessage-app-store-gatekeeper...). Meanwhile, some estimates put Bing's monthly active users over a billion.