I think this would work, but university prestige is often based on scarcity so few universities do. This is the same reason that Harvard has almost the same number of undergrads as they did 50 years ago, despite an endowment 20x the size.
But it is a combination of scarcity and quantity, interestingly.
By any measure that is per-student, Caltech grads for instance are far superior to the average MIT grad.
However, MIT has better name recognition and looks far better in stats like "number of publications in top journals" or "number of Nobel price winning alumni", just because it has five times as many researchers and pumps out five times as many alums every year. So the winning strategy is to get as big as possible - but only as long as the majority of your intake is still in the top half-percent of the bell curve...
That's a pretty broad statement. I can think of a number of measurements where MIT comes out ahead of Caltech - entrepreneurship (measured per-student) would be one particularly relevant to HN.
Cambridge is certainly no where near as expensive as say, New York, so by your logic Columbia should be smaller than it is? A significant portion of a school's ranking (and overall prestige) is the difficulty of admission and the yield, so schools have an incentive not to expend indefinitely (plus there are other advantages of small/medium size).