It just seems so arbitrary to choose to name the child after one side of the family every time - so you're part of a long, traceable line dating back to someone who forms only 1/128th, 1/256th, 1/512th (and so on) of your ancestry. Drawing that line so brightly seems to push everyone else who has contributed equally to your lineage further into the shade.
So it is with surnames of course. To combine the two, from the same thin line, seems so very unimaginative and so uber-patriarchal.
There have always been cultural and political reasons for and cultural capitulation to patriarchy of course. Does that mean we are and should be happy for this to continue? And cannot speak of it from the viewpoint afforded by a different culture? I don't see that privelege operating unchallenged in other areas of life.
More practically and swerving the political angle in favour of all round celebration and appreciation, why not mix it up a bit? Surname from one side, given name from the other?
I know a family where the mother's maiden name, or the grandmother's, has traditionally been given to boys as a middle name, as one variation. Girls' names referencing maternal grandparents is pretty common too. Why not boy's names referencing maternal grandparents?