I suspect that you put it well when you state that it is our society's "presumed negative view," since I suspect that it is a minority of people who actually do marry as virgins these days. So if our actual cultural values are reflected in our practices, then I think what we find is that only a minority actually share the negative view of which you speak. Truly, I think even where there is some sort of negative view, it falls within something of a double standard: We have a negative view about others engaging in pre-marital sex (especially if the others happen to be our daughters!), but we do not regard that view as applying to our own behavior. Anyway, I think that most people now realize that pre-marital sex is much more the norm than the exception, which is why it is more surprising to hear of someone in their late teens who has not yet had sex than to hear that they have. I'm not sure what the current statistics are, as to high schoolers, but obviously the percentage who have had sex will go up as their grade levels go up.
I also think that most actual instances of sexual activity are not "used for procreation," as you put it.
The origins of the prohibition in our culture may go back to the Bible, as you say, but I expect (as I have said in reply to another question recently), I actually think the prohibition falls more generally under the cultural norms that require monogamy, which I have specualed go back to the change from hunter-gatherer societies to agrarian ones, where the value of private property becomes extremely important, and now the idea that other people can also be made into private property also becomees salient to human beings. Hence, all forms of ownership of people, from slavery to notions that we can have our very own spouse and also regard our children as truly our own, and so on. A prohibition against pre-marital sex would simply derive ffrom this value--we don't want to own a spouse who is "used goods," and so came to expect the uses of our property to be entirely private to us. The biblical prohibition simply reflects this way of thinking and encodes it into doctrine.
I reckon some of my colleagues will think there is much more to this than I have proposed, so it would probably be wise for you to wait for other responses here!