At present it's possible to "add to home screen" on iOS which creates a nice icon, but you're limited to the unauthenticated view. It would be nice to be able to use it from the home screen like an app. Homebridge config ui x does this quite well as an example.
What "it" are you referring to.
There have been user shortcuts published, that work well with embedded login credentials. Is that what you are looking for?
For comparison. Homebridge homescreen launch vs pi-hole. When clicking on the homebridge link even one's login is maintained for some period of time. When clicking login in pi-hole you're then redirected back to safari.
What specifically are you adding to your IOS home screen? A shortcut to the browser link?
That is not unexpected, since Pi-Hole uses a browser based interface and not a separate Android or IOS app.
Pi-Hole will save your login credentials for 7 days via a check box option on the login screen.
Is your feature request for an Android or IOS app to interface with Pi-Hole?
Not asking for a native app, sir. That seems silly. Note that homebridge-config-ui-x is not a native iOS or Android app. It's also a web app. Lastly, yes, adding the Safari web link to the homescreen.
Thank you
If you are added the safari web link to the home screen, and if you have checked the box in Safari to save login for 7 days, is Safari not saving the login credentials?
How are you adding the shortcut to the home screen?
From safari http://192.168.1.253/admin/index.php and login checking the remember for 7 days. Then using the share sheet action to add to home screen. If this is not expected behavior, please tell me what I'm doing wrong. If it IS expected then I stand by my feature request. 
On the IOS home screen link to the bookmark, if you click login it will log you on with the stored credentials; you won't have to type anything. This is an IOS behavior that we cannot change with any Pi-Hole code changes.