Child marriage is surprisingly common in the world, and correlates strongly with strongly patriarchal (and culturally archaic) societies.
That is to say, ones that tend to enshrine male dominance over female agency as a cultural staple, to the point of females being considered property or chattels. (A great many forms of wickedness are possible, when one does not consider the recipient(s) as persons. This is an important lesson for current society, vis-a-vis the future evolution of AI, should it ever arrive. Humans will want to cling to the notion that the machines should serve without question, and a great many forms of wickedness will be around. In this case, we get to see the hold-overs from the bronze age cultural heritage of such regions, and how the view of women as non-persons without rights leads to great wickedness, as its parallel.)
I'd argue the other way. Those relationships exist in the existing economic framework. As the economy evolves then the tradition of those marriages falls away. The west didn't really have to outlaw such marriages to make them rare, they just became rare. As evidence, look at extremely wealthy Arab states, such as UAE, Kuwait and Qatar: they have a lower overall
gender age gap at marriage than the USA does, despite being extremely patriarchal and conservative, while places like Nigeria have a very high gap and a lot of those child marriages.
The economic realities that make such marriages a thing are low life expectancy, the need for large families and the long time required to become financially stable. If you need a big family then you either have more than one wife, or you have a young wife. In such a situation, if a new modern government comes in and does a census and cracks down on any polygamy situations, which may be traditional, then that would in fact push things economically to favoring a young wife, since she can produce enough kids to work the land: and for poor subsistence farmers this is borderline not even a choice. If you don't make the optimal choice, then you basically lose the race and your family farm is lost or absorbed into a different family who
did prioritize having more kids. You're being pressured by the grandparents to ensure you pop out at least 12 grandkids, because that will ensure good odds that 1-2 boys will survive to adulthood to carry on the family.
So if you don't want so many child marriages you need to make it so having a lot of kids is no longer a required thing you just have to do to survive. This also explains why it works one way but not the other. If you have a young girl marry an older man, he is at the point of having more economic value during the marriage (skills, strength, acquired resources), while she has a longer period of child-bearing possible. If you reverse that and have a young boy marry an older woman, what are the economic advantages of that, exactly? None, basically, which explains why it isn't a thing in any existing culture. So, that model doesn't actually require any tacit scheming to keep men in power, it's just the
economically more sensible arrangement, which is why it became widespread.