This still happens, not as much as in years past but it's still frequent in a lot of societies outside the 'western world' like in africa, arabia, pakistan, india, pacific-islands (like fiji).
I see your point. However, the issue is that a woman's last name is always her father/or a man's name and his father's name and so on but the man isn't marrying the father.
Even if they both decide on having double-barrelled names, then what happens if they have a daughter and she's getting married she'll have to have a triple or quadruple double-barrelled name because she can't leave out one of her last names that defeats the point of it being double-barrel in the first place.
Before you know it, everyone has double digit double-barrel last names.