The Google Maps situation is a great example of why this will be hard. When Apple switched to their own maps it was a huge failure resulting in a rare public apology from the company. In order to switch you have to be able to do absolutely everything that the previous solution offered without loss of quality. Given Google's competence in AI development that will be a high bar to meet.

several years after that they still have their own Maps though, they didn't go back to Google Maps.

Well, yeah, Apple's Maps.app wasn't good enough when it launched (it's solid now though). That feels like a separate thing from white labeling and lock-in. Obviously they would have to switch to something of similar or better quality or users will be upset.

But it's a whole lot easier to switch from Gemini to Claude or Gemini to a hypothetical good proprietary LLM if it's white label instead of "iOS with Gemini"

They switched despite Apple Maps having poor data for a reason:

Google wanted to shove ads in it. Apple refused and to switch.

Their hand was forced by that refusal.

The problem with the analogy is that users were asked to change their habits. Apple switching Siri models behind the scenes is much less problematic.

It wouldn't have gone any better if the original mapping solution had been a white-labeled "Apple Maps" secretly powered by Google Map.

I was in agreement with the parent before I read this, and now I'm in agreement with you. It is a great example, I know so many people who never switched back to Apple Maps because it was so poor initially. Personally I find it a considerably better experience than Google Maps these days, but those lost users still aren't coming back.