Our family is the opposite of yours... Partly because of euro heritage (no nudity = sex thing) and Asian upbringing, partly because of large families w/ limited bathrooms (4 kids and 2 adults all need to get clean), partly because we're active (camping, surfing, boating, swimming, etc... These and others all have relaxed strictures surrounding nudity/bathing whether it's gym showers or beach showers), partly because we're a mix of military and medical (again, nudity is no biggie).
But even though our family, and most of those I know from the above spheres and a few others take little issue with casual nudity... Most of this country is more puritanical.
Nothing wrong with either, IMHO, it's just what works best for each family. Which can also change with time. I have a girlfriend raised much as your kids are who had 5 kids and 1 bathroom. Nudity and piling as many people in the bath/shower as possible quickly became a way of life. Another has a son with special needs, and everyone helped there. Conversely, another ONLY gets her private time in the bath, so that time became sacred... Even though she didn't give a rip prior to having kids.
Different families, different needs.