Is a doctor considered negligent or excused if he sometimes misses the Friday prayer due to work circumstances in an American hospital, knowing that he cannot leave during working hours and repeatedly apologize to his superiors, and he will try not to miss it as much as possible?

Mere fear of not being permitted to leave to perform Jumu'ah prayer does not excuse you. Rather, you must attend it at the mosque, and Americans generally understand this. If, after attempting to leave, you are not permitted, then you are excused, and you should pray Dhuhr, four rak'ahs.