It’s important to point out the obvious: the replacement rate for academia is exactly 1 PhD student with faculty aspirations per lifetime of each professor. Anything >1 and academia must grow exponentially to accommodate every single PhD student who desires a faculty position. It is shocking how little this basic, obvious fact is discussed within our ivory towers.
Isn't it implied that only the best PhD students will get a faculty position? How do you choose the best one if you only let one student enter a PhD program?
This is particularly bad in academia because a lot of professors intentionally take on more PhD students than can possibly fill future roles for which a PhD is necessary, in order to use them as cheap labor. This is especially true in the biological sciences: rather than hiring career staff scientists to run experiments, professors simply use their much cheaper grad student labor pool.
What the exponent should be is a whole other matter.