Not any time soon, as iOS isn't very FLOSS friendly (in fact, the GPL is not compatible with the Apple app store). There have been talks of making a licensing exception, but the iOS client with the most progress (https://github.com/Jman012/Toxicity) isn't functional at the moment.

I believe there's someone working on a completely different iOS client that looks pretty snazzy, but they haven't got any public code in their repo yet.

MPLv2 is compatible with both the GPL and the App Store.

Oh, that's a shame. Hopefully in the future there will be an iOS client.

Ask Apple to change their policy to allow copyleft software.

It has nothing to do with Apple's policy. The GPL is what's getting in the way: it says you can't impose restrictions on the redistribution of a GPLed application, and the App Store doesn't have any means to even permit redistribution of apps once they're installed.

Seems like the App Store's problem.

Google play store doesn't have that problem.

Apple sells products which they have decided to retain control over after sale.

That is Apple's choice, Apple's policy, Apple's decision. It also conflict with a lot of things, including the GPL.