> Allowing more browser engines would require granting those engines your battery and gyroscope data in order for them to display per-site permission dialogs.

...a process which could be reviewed as part of the App Store review process.

There isn't really any difference here. If your app reads gyroscope data App Store review will (theoretically!) make sure you're not doing anything nefarious with it. They could just as easily verify whether a browser passes data through correctly.

Correct: they are not doing something that is possible to do. What benefits to their users result from that choice?

(I’m aware of what drawbacks result from it, but that’s been explained to death in a thousand replies in a hundred posts about this already, so no need to derail into them here.)

One benefit that immediately comes to mind is the ability to protect yourself against a major security flaw in Safari:

https://safarileaks.com/

Apple did issue a fix after a few weeks but with no alternative browser engines the only alternative was “don’t use the web on your iPhone”, which is absurd.

Other user benefits might include better performance, more capabilities (it took Apple years to implement WebRTC, for example) and in general more competition that might spur Safari into becoming a better browser.

The other browser engines have other security CVEs. Switching engines on the backend does not materially reduce the total attack surface for vulnerabilities for any given everyday user. Using security vulnerabilities as a primary condition of existence also leads to the introduction of engine oversight, review, and adamant “update or be removed” policy enforcement upon third parties, all of which who will complain endlessly in the press about the draconian App Store policies they would be subject to. I expect a better case will need to be made to convince Apple.

You asked:

> What benefits to their users result from that choice?

But now we've gotten to

> I expect a better case will need to be made to convince Apple

Those aren't nearly the same things. Of course it's difficult to convince Apple, it isn't in their interests.

You make the case that it’s to the benefit of their users to allow multiple browser engines. I am personally not convinced by your case, for the reasons stated above. I do not expect Apple to be convinced by your case either.

You may choose here to strengthen your argument, but your declaration that it’s hopeless to do so is of no help in that regard. If you wish to continue, I’m willing to listen.