I've ponder this question myself for quite some time and I still don't know for certain. When it comes to reproducing offspring I think that whole process is to combat diseases. You see bacteria and viruses have been around for ages and ages and to better protect ourselves from them we evolved to reproduce sexually. A male and a female both contribute 50% of their genes that create a new and unique genetic sequence that makes a new person that's why no two people are one in the same because of the many different combinations coming from males and female genes. Now regarding a much more significant purpose other than that, my theory is we are here to endure a world full of suffering, pain, fear, and injustice. Life in it of itself is a journey full of obstacles and hurdles that one must overcome and prevail or succumb to. I think we are supposed to either learn something or prove something and what the something is your guess is as good as mines.
I hope that you get many responses! If we approach Life with the idea that we should be Roman and take what we can, we get old and have no friends left (because we killed them and took their stuff) which isn't, really, that fun. If we "practice reproduction" to our heart's content, we get germy, really, really, germy and end up with no friends because we boinked every thing until EVERYone's feelings are hurt. If we shop and eat to endless joy, we get BROKE and have to have a scooter. So, after we eat and sleep and clean and deal with income, the best things left are Music and Sports! SPORTS are the MOST evolved form of war EVER!!!!!!!!!! MORE SPORTS FOR EVERY ONE!!!
But we should always make the most out of the time we have, since we're mortal beings. I, myself lack any desire to reproduce, so there's literally no purpose for me. I don't become depressed on the fact that the universe is pointless, or that we're a tiny spec in the literally infinite. I just try to make the most of it, just as we all should.
Heavens know I've met a bunch of people whose life is reduced by their own choice to destructive drives including inane sex.
It doesn't mean they can't do better of course, but they just won't even when prodded to do better. It's just the way there are.
So, not all lives have a greater purpose. And reproduction isn't a great purpose unless at the same time we put our potentials to use to create something greater.
After all even the cave men knew how to breed as well as all life forms.