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Chrome on Android will show a banner to add it to your home screen.

True, the situation on Android is much better than iOS. Also after you do this, you get an icon in your app drawer and not just the homescreen.

It also shows up as an app in the system menu, with natively controlled permissions, notifications, battery restrictions, etc.

iOS doesn’t have an app drawer, so I’m not quite sure where you’re going with your comparison…

Yep, sorry that was confusing. I was comparing to previous versions of Android. It's relatively new that it's added to the app drawer.