In order to reduce the number of teachers, while still teaching the same number of students, means either increasing the "teaching load" or the efficiency of the teaching needs to be increase.
Increases in teaching load require decreases in other job responsibilities. This is essentially the difference between teaching only colleges and research universities in the US and new and old universities in the UK. While teaching only colleges do not generally pay their faculty more, there is evidence/claims that having professors with active research benefits students.
One way to increase teaching efficiency is with larger classes. From my understanding moving from small seminars (10 students) to large seminars (40 students) is bad for student outcomes (again no change in how much faculty get paid). I am not sure if going from a 200 person lecture to a 400 person lecture has the same hit in learning outcomes, but logistically, most universities are lacking large (400+) lecture halls. Additionally, logistically, large classes often means less variety to students.
Another way to increase efficiency is for less contact hours (and to an extent less assignments requiring grading). The US and UK teaching models basically hit the extremes in terms of contact hours and grading. The US has lots of student contact and lots of small assessments compared to the UK. I do not know if there is any evidence that one system is better than another, but having US students switch at the university level would be difficult.