Whether we like it or not, President's like Clinton and Carter were still Presidents, elected by the people of this country to serve as CIC.
They should have boats named after them, as disgusting as that seems.
Only because that stupid tradition got started after Reagan. We didn't always reflexively name our carriers after presidents. The first was FDR, shortly after he died in office. Next was Kennedy. Same thing. Then Ike, who didn't die, but did command our forces in the field. Then we had TR, Lincoln, and Washington. More recently we had Truman, then Reagan, and the next is Bush. If we could get away from naming them after presidents entirely, we could avoid the embarassment of a William Jefferson Clinton. Sure the man was commander in chief, but he was also impeached. Name an oiler after the slickster.