How to change incoming call notification size in Nexus 5X
This smaller Caller ID banner does appear only when on the home screen and when using an application. I assume this was done so as not to cover the whole screen in case the user is doing something critical or the like. 

While on the lock screen, an incoming call will take the whole screen to show Caller ID, presumably because the user wouldn't be doing anything if the phone is locked.

I looked through my devices Phone and Accessibility and other settings, and I was not able to find any way to change this. A third party app would be your best bet.

Using Android 6.0.1 to test.