So there are additional layers of security which I appreciate. But this is different - the iCloud login prompt repeatedly pops up every now and again. Sometimes after an action, sometimes on its own. I had it before on my iPhone 6S when I upgraded iOS at some point ... then it randomly stopped.
I think that is a problem with session management across multiple backend systems that are not updated quickly enough when you are first setting up. Each one thinks that it is the first time you have authenticated.