Ah, just as I post my method of creating a shortcut with an icon of my choice on the iPhone home screen - which I demonstrated with Firefox - along comes a browser that allows a choice of icons out-of-the-box!
What timing! DuckDuckGo Privacy Browser starting with version 7.37.0, released on 31 Jan 2020, has a feature to customize the home screen app icon! Just select the background colour of your choice from Settings > App Icon:
So now I can satisfy my OCD:
Nice! Can more apps provide this? Hint: green background please.