Why can’t I order my icons alphabetically across all screens on my iPhone

You can go to Settings ➜ General ➜ Reset ➜ Reset Home Screen Layout

This will reset the Home screens and order all none Apple Apps alphabetically.

Apple apps will be placed in their default locations.

Note, that this destroys and custom folders you may have created.

As Mentioned, App Library, also offers and alphabetical list when you tap on the search field at the top.

click here ➜ Organize the Home Screen and App Library on your iPhone - Apple Support

There is no single button option that you can press and all the apps will be arranged alphabetically on your Home Screen(s). That feature does not exist. You can move the apps manually and arrange them alphabetically, however, I understand that this will be a cumbersome task. You can suggest this feature directly to Apple by leaving a product feedback here 👉 Product Feedback - Apple 

The other option is to use the App Library if you want to see your apps listed in alphabetical order. The App Library is the last Home Screen on your iPhone when you continue to SWIPE LEFT until you reach it. Once you are in the App Library, then you can tap on the Search Bar and all your apps will be listed alphabetically to start.

Axel F.

We can't answer why questions here on this user to user only forum. We don't work for Apple, nor did we have anything to do with how iOS works. Have you perhaps considered putting your apps in Folders, which makes it ever so easy to find an app? I have apps in folders, like Banking, Social Media, Automobile, Photo/Camera and thus when I need to find an app, they are grouped in folders for simple access.

Here's a link on how you can create folders for your apps --> Move apps and create folders on your iPhone, iPad, or iPod touch - Apple Support