Great to someone else ‘angry’ with Apple! FWIW I have been building web apps using the model prescribed in PWAs for about 7 years now. Short of true native push notifications you can, for the most part, ‘polyfil’ PWA features on legacy platforms (like Apple).
I don’t have enough space here for a full description, I mean I wrote a book on it 4 years ago LOL. But you can make sites work offline, and I know appCache sux the big one. But you can leverage storage, I used localStorage for the longest time and now migrating to IDB, for offline.

You should not need a splash screen if you architect your code correctly. Even unprimed you should be able to load any page over 3G on a crappy Android in 3–5 seconds. Once you cache assets in storage it should load in < 1s consistently. However, Fast Food Frameworks like Angular, React & Ember make that impossible due to the overhead they require.
There is a very popular library called Add To Home screen available on http://cubiq.org to help with the home screen prompting.
These techniques, polyfils, etc all help. The way I look at PWAs is the platforms are now making the architecture and techniques I started using out of necessity back in 2010 native. This means I have even more advantages when they are available. That is the goodness that progressive enhancement offers.
Since I adopted these techniques I have made many web apps that were faster than a native counterpart and offered simile overall UX. That is what customers care about.
Plus I could update the web app anytime I wanted and the businesses did not pay the Apple tax on sales.