A full answer, I suspect, is evolutionary and not merely cultural. Sex is pretty universally a more private activity than, say, eating. (I'm not the one to tell you why this is so, but I gather that it is.) By contrast, it's hard to see how hunting and warfare, which are obvious sources of our attitudes towards violence, could or would be carried out in much privacy. And it's not surprising that our culture (or any culture) might be more squeamish about publicizing private acts than public ones. But even if this does explain the greater censorship of sex than violence, it's not clear (as the statement of your question implies) that this should be so.

It depends what you mean by "ultimate purpose". Sex and all that goes with it (the associated pleasures, the urges, the courtship-instincts) has clearly evolved because of its role in reproduction. It wouldn't exist if it didn't play this role. So if something's "ultimate purpose" is to serve that role the playing of which led evolutionarily to its existence, then, yes, sex is ultimately for reproduction. This is true, I think, even though this notion of purpose is, I take it, problematic on evolutionary grounds. One complication is that a thing (a process, a feature, a characteristic) may be a mere evolutionary by-product, and so not have a purpose in this sense. Moreover, things that evolve for one reason might start to serve new purposes, and persist and spread because of this. And finally a thing's evolutionary purpose(s) (if any) might be entirely indiscernible to us. I presume, though, that none of this applies to sex. In fact, sex is probably the only thing that I (from my armchair) feel...