Caller ID not working even after a week and 5 tech chats with AT&T

I added an iPhone 5 for my dad onto my family plan, but his Caller ID is not working. The number still shows up as "Unknown Caller" when he calls another iPhone (landlines seem OK). I've had 5 tech chats with AT&T and was reassured each time that the problem was solved--but not so. Told it was either a mismatched ICCID, a default "disable Caller ID" setting, etc. Getting frustrated.

Would I do a full "Erase All Content and Settings" help? Or will that screw up the AT&T account settings, stored number, etc.? Really don't want to set myself further back and do 10 more useless tech chats just to get back to square one. Thanks.