I meant a long time ago, when these institutions first developed among humans. The fact that paternity tests exist now probably only corroborates my point. I'll edit the comment for clarity.
It's an important distinction. The desire for fidelity is clearly genetic. I agree with you, it probably entered the gene pool because of those reasons. With those reasons now gone, it can and probably will exit the gene pool. This will drastically change the nature of human relationships.
Yes, I think we agree fully. I would add that the persistence of norms does not have to be directly genetic in the way most people would interpret that. It could be indirectly genetic, in the sense that we have a strong genetic propensity to adopt the norms of our social surroundings and attempt to spread those norms to the next generation. That propensity probably applies even for norms that have far outlived their original purpose.
I don't think the reasons are gone completely. Having children is much more than mating with someone and taking a test to determine that the children are yours. I want to have children one day, so I'm very careful with who I select for a partner, because I want her to be there with me raising our children, and be very committed to the family.