You can save any website to the Home screen as an icon, and you can even remove Safari chrome from it. You're just giving up app discovery through App Store.
I suspect they want the app to have an easy access icon on their home screen. I don't think most people know you can save a shortcut as an icon from a given web page on their home screen.
Also, an app is there, with an icon on the home screen to remind the user of its existence. I think this makes future use more likely than if the user just entered the address, and even more than with a bookmark that is visible only in the browser.
I know the users can create the icon themselves by saving a bookmark to the home screen, but for some reason they seem not to.
I have observed that non-tech people find the App Icons sitting on their home screens to be very convenient to access a service they use, kinda like bookmarks.
I use olauncher which has a super minimalist home screen. It doesn't block apps but it doesn't use icons. Instead you type the name of the app you want which I find makes me more purposeful with my phone usage. Turning off notifications for virtually every app also helps. If it's truly important I'll check it. Otherwise it's something I can look at once a day/week/month depending on the app.
I think you and all the replies to the parent have missed the point trying to be made. If you view the homescreens in iOS as your desktop, you don't want all your apps littering it with shortcuts. The op is talking about having to setup folders to hide away apps that they use rarely but don't want to uninstall. Android handles this in a far better way, where you have an app drawer that pulls up all your app icons on a grid that is easily searchable if you want to get to any installed app. That frees up your homescreen to be used for exactly those icons and widgets that you want, which is a lot nicer than the iOS way.
It's worth noting that Android solved this problem a long time ago. Home screen shortcuts just open in whatever browser you created the shortcut with. If apple hasn't fixed this a year from now, it'll be a clear indication that they are taking this as an opportunity to disadvantage the web platform.
You can also bring up the task tray, press and hold the icon for safari(or any other app) like you would for moving apps on the home screen, then press the - sign that appears to close it. Discovered it by accident, but it's quite useful.
The other downside is that even if mobile websites encouraged people to use the “Add to Home Screen” ability to the point it became somewhat popular, Apple and Google could just remove the ability all together in an OS release for “reasons” leaving users SOL.
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