So I don't want my following paragraph to come across as stating a direct connection, just as some information to draw your own conclusion.

You can take any group of men and give them a bunch of sticks and call it an army. But a navy takes years to build and train officers for. This often leads to naval officers requiring higher education particular in technical subjects that an army officer doesn't need as much. Higher education at universities and military academies leads to tight knit connections that carry on to post military life, help children get head starts and continue the "old boys network". It also means that wealthy connected non military men often want their young sons in the navy rather than the army if they have no choice during times of conscription.

For JFK, he was rejected for Army Officer Candidate school on health grounds (funny how being enlisted was never an option for JFK). So his father, who ran a shipyard in WW1, was first chair of the maritime commission and was a friend of then Secretary of the Navy Franklin Delano Roosevelt managed to pull some strings to get him accepted into the navy.

After a short stint working a desk his father pulled more strings to get him into PT boat training which would let him as a junior officer command his own ship instead of being one of many officers on a larger ship. This means JFK's name got attached to the victories of his ship giving him a much larger public persona than other naval officers that contributed to his political career.

LBJ was a congressman before ww2 where he served on the Naval affairs committee before military service in the navy. I imagine that previous political experience played a part in the choice of military service.

HW Bush family had no direct connection to the navy, but a father and grandfather politician probably helped in him being an officer, not enlisted.

Nixon had an exemption for military service due to his government work, so got to choose his branch and mode of service while Ford initially enlisted in the navy after pearl harbor, his law degree quickly turned that into an officers commission.

Compare this to Eisenhower who had to take years off in college to work to afford tuition and his application to the Naval academy was financially motivated. He was rejected for the naval academy but accepted by the army academy instead.

Simply put, the Navy boys had far better political connections than the Army boys.