Therefore, it's not Apple's problem. In fact, I've talked to a non-trivial amount of engineers (both in Cupertino and long time Cocoa devs) that disapprove of the shortcuts that Cocoapods takes all over, software architecture be damned. Reasonable parties can agree to disagree, but I do include 3rd party framework inclusion without a dependency manager as an interview screen for prospective iOS hires.
Since you mention developer relations, I'll assume you're not actually arguing that this is Apple's technical responsibility, but that they should throw around some $ to grease the wheels to make dependency inclusion better. As a platform vendor, funding hosting costs for some project that you don't agree with just to "support the community" is a bad idea. Better idea is to allocate resources to setup a structure that can fix the issue in a technically agreeable way while also benefitting from the independence a FOSS project provides. In doing so, you are correct that it'd be preferable for Apple to fund/use well-known FOSS standards, such as Github.
In conclusion, Apple should setup a FOSS project to address the current inconveniences associated with third party package inclusion and should involve and pay Github somehow.