Dryness is the difference. Yes, synthetics will get damp. But they still warm when damp, and they don't hold water. Instead they move it towards the outside. Provided all layers do that and the outside membrane is breathable it will dry quickly. I've dunked my whole arm and had it bone dry within a half hour.
Cotton soaks up a lot of water, holds it, and has no insulation when it does.
As a little experiment, wash a similar weight poly base layer with a cotton long John. Notice weight difference coming out of machine. The cotton is holding many times as much water. Now hang and air dry. The poly will be dry in an hour or two if the humidity is low. The cotton may take a day or more in the same conditions.
Anyway, the synthetic system only works if every layer is synthetic, and the outer layer is breathable. Otherwise the whole shebang just doesn't work. A cotton layer over a synthetic layer just absolutely soaks the cotton in short order.
And it's all expensive. So if you don't want to do the whole system, go with wool. Insulates even when wet. Plays nicer in conjunction with non technical fabrics.
