The current experience of adding a shortcut to the Home Screen is the same from the first versions of iPhoneOS and there a lot of use cases for a better user experience for current websites and apps:
Do not let the user add the same shortcut more than once if it's the same start_url or current URL if no manifest is defined
Promote Add to the Home Screen for webapps that are using display: standalone in the Web App Manifest and/or having a Service Worker registered, similar to other engines: Chromium and Gecko with the PWA Installability Criteria, or if not, implement the beforeinstallprompt event from the Web App Manifest spec