JFK was an interesting man but many of your facts are in error. Profiles in Courage was ghost written. His PT boat was not run over accidentally but rammed.
It is true that he wanted to get into combat which he used political influence to get a command.
All in all, one of the best of the Kennedys, but he also had an affair with an East German spy.
As to the PT 109 thing, I've read a lot on both sides of that one. The captain of the Amagiri stated he never saw the PT 109. Some sailors claimed they did. The PT 109 was another bizarre twist in the JFK story. After getting command of the 109, he and his crew spent the first couple of months getting it in shape. His boat was run over or rammed less than a month into his first combat assignment. While it became a WWII legend, when it actually happened the possibility of a court martial was an open question. To the Navy, losing your ship is never a good thing. Losing a more maneuverable boat by being run over by a vessel five times your size and not realizing it was there until it was too late to get out of the way and never firing a shot is definitely bad. IIRC, the Navy investigation was an oddity, as the official inquiry was closed without reaching a conclusion as to fault on the sinking of the vessel. There are rumors that Joseph Kennedy again pulled strings to keep the sinking of the 109 from damaging JFKs military record.
It's hard to know what is true when researching JFK. In the PT 109 incident, some accounts paint him as the brave hero who rescued a crew member by swimming two miles dragging him by a strap between his teeth. Other accounts describe a man who was derelict, a rich yacht boy playing sailor who recklessly lost his ship a month into command. I think he was probably not a very competent officer, but he was there. He fought to get one of the most dangerous naval assignments and did his best, which wasn't that good. In Kennedy's defense, while Joseph pushed the media to turn the incident into some great naval tale, JFK never bragged about his war experience. When asked, he would say, "I was on a boat; it sunk."
JFK also fought to be reassigned to the PT Boats, but was declined. I know part of it was because of his back injury, which pained him the rest of his life, but I've always wondered if the Pacific command also pushed back because he was a liability in the combat theater. Incompetent enlisted men can be hidden. Incompetent officers can do a lot of damage.