I was once supervising 4 solo students in the visual circuit who were coping just fine, sticking to the rules and not getting in each others' way. Then a fifth aircraft announced that it was 'joining visual, straight-in'....
I told the controller to advise it that there were 3 in the circuit, one about to land and to 'join deadside'.
Which it did, fitting in and landing off its first approach.
It was a Queen's Flight corgi-carrier 146 positioning back after ferrying Air Miles Andy to some pi$$-up or other. The captain saw my CFI in the bar and tried to make some snide comment, only to be told to read the Flying Order Book and to be grateful that he wasn't told to hold off with the circuit full.
The visual circuit should be predictable; my teaching was never to extend beyond a point which corresponded to base leg for a flapless circuit, if that was looking unlikely then go around at circuit height and cross to the dead side.
Joining straight-in and calling final from outside the ATZ is only ever acceptable if there's no other traffic.