Back when? Girls usually reach puberty when they have reached a certain height and weight. With proper nutrition, girls are now reaching puberty earlier than every before. Your pedo fantasies are quite wrong.
In some countries in Africa, girls are marrying older men right now, and are expected to have children. Somehow their tiny frames can't handle the arduous stress and pressure of carrying a fetus and giving birth, and many of them die in the process. So the men are left with infants, but no mother to care for them, and they marry even younger girls, who also die during child-birth... The ignorance is forcing girls to give birth before they are mentally and physically ready to care for the children, and the stigma is old men having to care for infants on their own.
A meaningful relationship is something you have BEFORE having children, dolt. If you share interests and friends, like the same movies and music, make each other laugh, and cook delicious meals for each other, then I would agree that you do have a meaningful relationship. If the man sit around with other men and smoke all day long, while leaving their pre-pubescent wife to cock and clean and care for her siblings and children, and the children of her now-dead predecessor wives, then no, there is nothing meaningful whatsoever with your relationship.
Besides, if an older man and a child-wife really do have a meaningful relationship, they can entertain it over the net, or some other distant way, until the woman is over 18 and able to both marry legally, and have children without risking her life (all pregnancies are though and dangerous, of course, but if you're over 18, your chance of surviving is usually well over 50 percent).