Go to wondering one day about the no call sign issue so when Tater was traveling back from the west coast I went to "Live ATC" where you can listen to the radio comms in any sector you want. In this case it was the high altitude sectors, I wanted to see if not only the crew was using the AF1 callsign but also if ARTCC was acknowledging the callsign. And they were. On both accounts.
Even though the call sign is not listed on the flight plan per say, the crew of AF1 checks on to every center frequency as:
"Denver Center, AF1 checking on at Flight Level 380".
Denver Center: AF1 Roger, Flight level 380
Denver Center hands AF1 off to Kanas City Center.
Denver Center: "AF1, Contact Kanas City Center on frequency 134.8".
AF1: Kanas City on 134.8 Great day Y'all".
Possible that it's a security thing with not listing the callsign or maybe it's something else. Without knowing what is listed as the callsign on the actual flight plan, I don't have an answer as to why but could be that Tater is exactly what we all think he is and is not the CIC and ATC and the AF1 crew carry on business as usual in comms.