"[A] substantial part of the membrane has to be occupied [by sugar transporters] just to provide the necessary carbon even under conservative assumptions."

http://book.bionumbers.org/what-are-the-rates-of-membrane-transporters/

Yes I feel so, density of nutrient transporters embedded olasmalemma of cell wall contributes towards the selective uptake of different nutrients..

Is there any experimental evidence for this? I understand that intuitively it should increase, but has it been established experimentally?

Let's say i own a factory and i want to increase the production . . . i can hire more workers and/or tell them to work faster.