My opinion, about the posted picture and the original question:
It's great when the background contributes to the image. But it's more important that the background does not
detract from it, mainly by being distracting.
One way this happens is with bright things which get our attention. In the picture of your nephew and his fiance, the bright object on the right is tonally consistent with the couple, so it draws the eye (ok, maybe just my eye) away from the couple. If the object represents something about their relationship, this is a good thing, and we would want to be able to tell what it is. But if it does not have any connection, it shouldn't pull me away from them.
Another way something can be distracting is when objects in the background seem to "interact" with the subject when they shouldn't. A typical situation is having a pole sticking out of someone's head, like a telephone pole or fence post. The two things near your nephew's head do that
slightly. Back to your original question, if you are taking pictures in front of trees with no leaves, you would want to be very careful about this. If there were leaves, a slightly blurred background would be much less distracting.
A third way would be if the background is too "busy". If there's a lot going on, we start to wonder about it, even if we aren't "supposed" to. That isn't really an issue here, but again to your original question, it could be if you take a picture in front of a forest with no leaves.
I think the picture you posted is very compelling, and the background issues only knocks it down a little, like from a "9" to an "8". I'm not the "fix it in post" person, but because the subject is so well depicted, this might be a case where I suggest that: darken the object on the right a little, and blend the two poles near your nephew's head a little, and the picture may become even stronger.
Of course, since this is just an opinion, I won't argue if someone else's is different. :-)