So the tradition of naming CV's after Presidents is rather new overall, it only began after FDR died. The Midway class carrier Coral Sea was then renamed to honor the late President.

Since then the President's who were in good standing and with some connection to the military, especially the Navy nearly always got a ship of some sort. JFK got a carrier, so did Ike, Truman, HW Bush, and Reagan. All of which were still in commission at the time of the selection, though the conventionally powered JFK has been decommissioned and a new one will follow the Ford as CVN-79 while CVN-80 will be a new USS Enterprise. Jimmy Carter got a sub as he had been involved in work on early nuclear subs following his graduation from Annapolis.

So Ford was one of the last 2 Presidents post WW2 with some time passing that wasnt Nixon not to have a ship, the other being LBJ. He was also a former naval officer having served in combat aboard aboard the escort carrier USS Monterrey in the Pacific. While it should be noted it was a fellow Republican President in charge at the time, and a SECDEF in Donald Rumsfeld who had filled the same role for Ford and also for a year served as Ford's White House Chief of Staff. To say they were confidants would be underselling their relationship.

While the other main competitor for the CVN-78 name, USS America would go to a new class of Amphibious Assault ships. LBJ then while having technically served as an officer in the Navy Reserve had gotten the commission through pull as a sitting Congressman and only spent 6 months on active duty, mostly on an inspection tour as envoy from FDR to the South Pacific. He too would eventually get a ship as the 3rd hull of the Zumwalt class destroyer will be the USS Lyndon B. Johnson. In general too while the fact that the lead ship will give name to the entire class is at least something to consider it is rarely an overriding consideration in ship name choices, and politically fashionable picks, funding battles, and personal preference all have large roles.