You say a family benefits from all children having the same name. How? Why?
"Oh, Ms. Jones, how nice to meet you. And I am especially happy to meet you, Mr. Rockefeller. How's your dad?" "Oh, you say you're siblings? How interesting! Does Mr. R. acknowledge you, Ms. Jones?"
This is trivial. In any community where kids are privileged by their parents' contribution - i.e. every community - one member of the family is likely to be more prominent that the other, and the family name benefits everyone carrying it. Today, that person is most often the man of the house. If the facts on the ground change, maybe the family name should change, too. (But see the next paragraph.)
Why isn't it the female's last name? Probably because maternity is obvious and paternity must be acknowledged. Biology creates paths of least resistance that wokism tries to by-pass by denying their existence. But a girl with her mother's name may or may not be a bastard in her father's opinion.
Yes, of course it's a bad thing that only elitists plan their social systems with "rational" thought. Any army lifer will tell you that the Army is a system designed by geniuses to be run by idiots. A system designed by geniuses to be implemented by geniuses is, as I said, classist.
The issue isn't rationality. The designers of the current system are rational. The issue is reading the room. Social systems must work for people who do not have the wherewithal to design them. There is no suggestion in my post that rational thinking is a bad thing, but there is a suggestion that rational thinking can proceed from flawed premises about the nature of the world.
Most people act logically in some sphere of behavior. But, again, "logical" thinking is about what one does with premises, not about whether premises are valid.
Whether I am praising or denigrating anyone is wholly beside the point. The world is as it is, not as people of good will wish it were. That's not to say things can't change, only that a material basis for their being changed should be offered. In my veiw, you are the one who has not laid the groundwork for your solution.
There is no "therefore" in Mencken's quote, much as you would like to read one in. He's just making an observation about how little vetting people put into their easy fixes. Your solution is not necessarily wrong because it is simple and plausible, but it is unduly appealing for that reason, and unduly appealing arguments tend not the carefully critiqued by their proponents.
I'm satisfied that I have said enough to persuade careful and thoughtful readers that your solution won't work. Whether I have in fact supported my claims is for each reader to decide. I can live with your not being convinced.
BTW, you don't get to decide what I mean by "elitist." If you don't like the word choice, that's fine, but you know damn well that I am talking about intellectuals who think the world has an infinite capacity to absorb and practice their intellectually intensive schemes.