Keep in mind that when the word "shift" is thrown around, that's the bare minimum you are going to be there before you can check out. On wards, we can theoretically check out if we're on short call at 7 pm.... but I've been there many nights until 11:30 because a patient was sick or because I still had H&Ps to write. In the ED, we do 12 hour "shifts" but then usually have a couple hours worth of notes to do after. And even though I love shorter hours, I hate the mentality that comes with the word "shifts." When an intern is checking out while one of their patients is going downhill on the floor because "hey, it's 7 pm and time for me to leave," that is not ok. It's also not ok to be taking short call and be responsible for your team's patients and tell the night team "eh, I don't know anything about them. They're not my patient." Usually, at night, there are way fewer people than during the day taking care of patients (for instance, we have 2 people caring for the number of patients that 15-20 people care for during the day; average about 45-75 patients per person on night float); it's never going to be quite equivalent because you can't possibly know every patient well on nights when you're caring for so many, and it's not a 1:1 person shift change like it is for things like nursing.
Also, doctors are tired because we average 4 days off a month (and may go a couple weeks in between a day off) and, while in the hospital, it can be physically, emotionally, and mentally exhausting a lot of days, which exhausts you way faster than you would expect. It's a different kind of tired than most people are used to. And our schedules change constantly from day to night float without much time to adjust.