It's not just a safari problem, last I checked Chrome on iOS also does not support service workers, so you're just helping Android users.
Apple has a vested interest in pushing users towards their walled garden for apps, while Google and Mozilla are trying to bring app-like experiences to the browser. There are hints of Safari supporting serviceworkers but I'm not holding my breath.
While true, the most compelling use-case for serviceworkers is still on mobile. Serviceworkers solve the problem of intermittent connectivity. They can patch the gap when a user drops a connection for less than a few minutes (e.g. when a user is mobile).
Laptops and desktops still benefit, but less so because generally if you sit down to use one of those devices in an area of poor connectivity, you're going to run out of things you can do with your serviceworker's cached content pretty quickly. If you're developing a serviceworker, the improved experience will be most felt by mobile users.
That depends on the application. Some applications will run out of stuff to do after a few minutes offline, but others (especially where individual tasks are pretty independent, like Google Docs) can still be very useful for long periods, and can benefit from increased control of caching strategies.
Unfortunately for Edge/Windows, in order to make the app installable it will have to be registered in the Windows Store. A small nuisance, and maybe a compromise that Safari/OSX could move towards, but still a pointless exercise that misses the point of PWAs.
The Guardian has an experimental iOS app that polyfills the Service Worker API. The way you'd use it is, roughly, change the INITIAL_URL variable to your home page, change the name / icon / etc. of the app, then release it on the App Store as an actual app.
If you have an actual iOS app already, then this is of course worse, but if you have something that works nicely as a webpage on Android with ServiceWorkers and you want iOS users to have some option at all, this is probably worth playing with.
