It will need Apple to introduce in Safari the same kind of prompts that Google has introduced in Chrome, to make saving to the home screen discoverable. At the moment there is no clear distinction on iOS between saving a standard web page to the home screen and saving a PWA, and a non-expert user simply won't make the conceptual leap to thinking of the PWA as an app.
All this seems quite carefully calculated by Apple, not to miss the boat on service workers, but also to hamstring PWA's just enough to make them non-competitive.
I think the most interesting area is apps which are written with web technologies, and then deployed to different platforms. For example, that could be a React Native codebase which renders to Android's native toolkit, iOS native, and HTML, and through that to a PWA and perhaps a Windows UWP app. There's a lot of flexibility there, to start just on HTML, or just on the native toolkits, and expand organically as appropriate.
Under the current circumstances, businesses will certainly want to be on the app stores, but there are a lot of services where just having an app is limiting, for instance I was looking recently at banking services for amalgamating accounts, and every one that I could find available in the UK has a website which is just a marketing page with a link to Google Play and the iOS Appstore. But surely most people also want to be able to look at their bank accounts on their computer, not everyone owns and iPad and a smartphone is a small form factor for that kind of information. A PWA, responsive, installable and offline-capable, is a good way of handling that.
I think, PWA will probably end up being a third target, not a replacement for Android or iOS.