Give Tom a break. He got forced into being the nurse because he took biochemistry classes before getting kicked out of the academy.
Plus, he's juggling nursing duties with his full time job as the pilot. And his side gig as a commando team leader. While moonlighting as a spy. And despite all that he's still finds the time to develop an encyclopedic knowledge of twentieth century earth. And let's not forget that he also designed engines with a top speed of infinity. He's the most competent man in Star Fleet. Not bad for a dropout and ex-con.
Pretty sure if you Tuvixed Paris and O'Brian, combining Paris's competence with O'Brian's work ethic, you'd get some sort of god.