Can I automatically arrange the icons of the home screen according to the frequency of use?
No, Apple doesn’t support changing or replacing the homescreen layout from within any app, including Shortcuts as of iOS 13.2.

I do however hope that they’ll open this up at some point in the future. Stuff like this is possible on Android or a jailbroken iOS.

Perhaps, the Siri shortcuts widget might help you with this though. It won’t do exactly what you want, but it’ll show some apps that it thinks you’re most likely to open next. You can also get to that by swiping down on your home screen to reveal spotlight search. There, you could then search for any app that Siri doesn’t auto-suggest.