However, for a company like Apple to change its stance would take a long time. Culture is sticky and, furthermore, they simply don't have the mass data collection and processing pipelines necessary for such an about face. There would be a fairly long period (my guess is years) during which consumers would be able to change providers.
I think the primary security white paper describes exactly how it works, but essentially there's a set of shared symmetric keys that are encrypted to public keys for each of your devices. Outside of the key vault path, the way a new device gets access to those keys is one of your other 2fa devices encrypt a decryption key to the new device when you approve it. The basic result is that there is no point in which the key material is transmitted unencrypted off a device.
This is only true for certain services.
But there's also a huge security benefit to apple not tracking this information: A hacker/angry-former-employee/creepy-current-employee can't access it either (eg. like the various stories we here about fb,uber,etc admins and employees spying on people).
Apple is in a unique position where they can sell hardware at profit making prices to a huge customer base. Even if we are at peak iPhone, current Apple users are not going anywhere (I tried to switch my wife to an Android phone once and it was a disaster hah). Privacy moves like Apple ID will only solidify the current user base. Best in class products like AirPods and the AppleWatch also lock users in - in a good way though.
I've noticed that since this announcement it is also pulling some stout Android users I know who have become disillusioned with how Google is slowly locking Android down. The constant bad press Google has received combined with the Apple privacy drum beat is starting to pay dividends for Apple.
I feel of all the major tech companies, Apple is way more invested in retaining their brand image.
...up until Apple decides to change their leadership, or their business model, or the mobile market implodes and they start looking for new revenue streams, or their relationship with the US government changes, or ...
I get that as a practical matter we are forced to trust somebody somewhere eventually, but at best we should be saying that "Apple doesn't seem motivated to abuse this information for now."