If you had to choose only one of these three, which of these "lovestyles" makes the most sense from a biological perspective?
polyandry - love for many men. The woman has more than one husband. polygyny - love for many women. The man has more than one wife. polyamory - love for many. Many loves for either gender.
The biological perspective needs to be taken in view of the sociological context. If you are just talking about pure biology, in reference to procreating, then they all would serve some purpose. But it is meaningless without looking at the sociological ramifications.
"I love the man that can smile in trouble, that can gather strength from distress, and grow brave by reflection. 'Tis the business of little minds to shrink, but he whose heart is firm, and whose conscience approves his conduct, will pursue his principles unto death. "Thomas Paine
Yes, there are some "enlightened" people out there that can have "open relationships" that are actually stable...
Pardon me, but I have never ever known anyone that's ever been in an "open relationship" that lasted. Usually, just a few months in and complications would arise. The couples that started out their "open relationships" started out telling the rest of us that they'd have no problem and blah blah blah. Just a few months in and there were fights over matters such as double dipping and not paying enough attention to each other.
Added by edit.
In other words, I've never actually seen or heard of an open relationship that actually worked in the long run. Until there's proof that it CAN work, I'm going to believe otherwise.
The point is that monogamy is just one of a broad suite of strategies in play for various species that invest heavily in the rearing of juveniles.
Shinigami's original comments were specifically about the human species. Your points about insect reproductive strategies are not related to that. Furthermore, elephants are not polyandrous: they are polygynous.
Polyandry can work for species that can lay many eggs in a short period of time, and for species that do not invest in caring for their offspring. But, neither of these things is physiologically feasible for humans, so we're not likely to benefit evolutionarily from polyandry.