] I agree, pure white is, even if you were mega rich. However pale, lightish fabrics with no significant pattern or embellishment were still the norm for young women to wear, they were cheaper to produce and to buy.
Actually, if you look at extant garments, that is to say garments of 1800-1820 that have survived until today, the everyday ones are often made of fairly dark prints. There was a whole range of dark, useful colors that were block-printed, then roller-printed (as technology progressed) with busy little non-dirt-showing designs. See my (needs-updating) page on fabrics for more examples.