Ford was a serving USN officer. Cant remember what Carter did, but think he served. LBJ was also in the USN (I think, or maybe Army) as some sort of made up number for the war at some point, but did fly in a dangerous combat mission in the Pacific.
Obama would make it onto my carrier list, no problem. He's clever, cold, calculating and very ruthless, has no problem doing whatever it takes to get his and the USA's way in the world. He's kept a concentration camp going, carried on with a war, led and helped start or try and start new wars (Libya and Syria and possibly in the future the Ukraine, Taiwan, Yemen, N Korea, Somalia, N Ethiopia, Pakistan) spied on his allies, carried out repeated drone strikes (now practically worldwide) on his enemies regardless of the by-catch. Good record so far. Surely up there from a what, nasty winning at all cost sort of bloke? Got to be on the list from a military winning waypoint>?
If you get one for being a 20th C prez, why isn't Carter on it? (the carrier list). Why not LBJ? Are they deemed as failures and not worthy?
What's in a name anyway? Ours are what, HM the Queen (increasingly very harmless gentle much loved but occasionally slightly waspy old lady whose done her duty to the max), and Prince Charles (is that the one that will be instantly mothballed? I'm not going there).
Think I would have been tempted to have called one of them HMS Trumpton, to reflect upon harmless gentle make believe nostalgia that reflected on a long ago, long gone Britain. (Google Trumpton, cousins).