It's become increasingly difficult for children to grow up without being exposed to very detailed sexual knowledge. When I was growing up, I think it would have been possible if a person was homeschooled, but these days with the internet and how much sex is on TV and popular culture, I don't know.
I think it's worth it for parents to at least try to keep their kids innocent for as long as possible. That would require very careful selection and monitoring of what their kids are exposed to on the internet and TV. Their kids should not be given unlimited access to either. Then, parents would need to ensure their kids are only friends with other kids who are being raised in a similar way, and obviously homeschool their kids so they aren't exposed to state sex ed curricula.
Now the question becomes, how desirable is it to keep kids innocent of sex until 18? I think the answer is not very. Sooner or later these kids will "leave the nest" and even if a parent's desire is to keep their kids from having sex until marriage, keeping them totally ignorant of sex is probably not the best way to go about that. They're probably going to run into somebody very quickly out in the real world who will tell them all about sex, and more importantly, give them a set of beliefs about sex that very probably go against the sexual values of their parents.
If the desire is simply to keep kids from having sex, the way to do that is to have an open dialog about the parents' sexual morality and values starting from a relatively early age. It can start naturally in early childhood with parents telling their children their private parts are private and that kids should not allow anyone to touch them there. Then, a little bit before puberty, this education can be expanded to talk about what the genitals are for, but explaining that just because they can be used in a certain way does not mean they should be used outside of whatever specific contexts the parents deem appropriate and healthy, such as marriage. Parents can caution their children against the use of pornography, and take steps to ensure their children aren't exposed to it inadvertently, or if they are, be there to immediately help the child put that pornography in context.
Kids will naturally want to know what their parents think about sex, and having a dialog with one's kids is the way to ensure kids learn the right lessons about sex. Parents who tell their children nothing at all about sex instill no sexual values into their children. Somebody else will inevitably fill that void. If the goal is to instill values, that has to be a thing done early and often through a child's childhood and well into the teenage years and young adulthood. It's been shown, for example, that girls that are particularly receptive to what their fathers teach them about sex. The same is true of boys learning from their mothers. It's a myth that kids reject their parents' values in the teenage years. They only do that if their parents (as many do) stop reinforcing those values out of either fear, disinterest, or absence.