You absolutely can control who your offspring choose. My daughter sees me loving a Black man, she has so many examples of strong, long Black marriages from most of her adult family members on my and her fathers side. she attends Black functions, has already made up her mind to attend an HBCU (my alma), is sure in herself as a Black girl and understand the plights of Black people and still would choose to be Black despite them. I don’t have to wonder if she will marry Black. Some Black people just get it.
Can? Sure it's possible but unlikely. The vast majority of American households are living paycheck to paycheck, if you filter to black people the stats get worse. Do you really think parents have the time and energy to monitor their children like that and hope whatever they instilled as a child kept?
In London there is a steep decline between public and private schools, and I know a couple black single mothers who work multiple jobs just so their kids can attend private schools and tutors. So, outside of ensuring their well being is good, grades are great and that they're well-adjusted I can't imagine these parents really have the time to "take actions that ensure a continued black lineage".
Then there's a matter of culture. Where I live most black people are children of African immigrants. The parents sometimes have a tendency to be harsh. But really it depends on the culture, the only thing they care about is whether you're bringing in good grades and that you're not fukking up or disrespecting the family. In fact the majority of guys I've seen wife a WW tend to be of African descent. In any case the end result is that culture, educational and professional success is put in front and stuff like blackness isn't really talked about.
Besides what are we talking about? A person's child (direct descendant) or their lineage going forward?
You can say that you control your kid or steer them to a black marriage but that sway deteriorates after a generation.

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