Baseball, perhaps because it is meant to be The American Game, does seem to discuss this question at least annually. I've heard no such wringing of hands that African Americans/Blacks are over-represented in the NFL or NBA. And I'm old enough to remember such discussion in the '60's about how Blacks were over-represented in the MLB; and that discussion was by Black leaders and academicians, concerned that young Black men saw their race over-represented in professional sports and in entertainment, and were therefore being provided with primarily unrealistic role models.
I've heard the 8% and 3% figures quoted before, but I don't know what basis is used for the distinction. Is Edgar Rentaria, for example, only Latin, or is he Black as well? How can one be designated by heritage, ignoring race? (If that's the case, my son isn't white, he's British.) Aren't there really more Black players than the narrow definition is computing? Is the distinction because the term is African American, and not African Dominican?
We've got a guy in our office who immigrated from South Afica. White guy, known to use the k-word. As far as the US government is concerned, he's an African American.
Robinson, and those that followed, quite rightly want to see that their struggle wasn't for the short term and they want to see their race represented in the sport they love. But their struggle far exceeded the white lines. Dr. King spoke of how Robinson's actions paved the way for the Civil Rights movement. That Black players were already important in MLB meant that the integration of the NBA and professional football leagues was more assumed than a fight. Their accomplishment shouldn't be diminished by associating it solely with the MLB.
As with any social question, all sorts of answers might be postulated:
Single Moms? Yup, those single Moms are known to sit down with their boys and tell football and basketball stories to impart a love of the game; I know I've had to stop myself.
Not enough space? Football requires a significant expanse of green.
Money for equipment? Again, football requires a significant amount of equipment per player.
Perhaps the pendulum has swung, and the number of Black kids who want to play are playing.
Unless somebody can come up with some evidence that the kids are being dissuaded or prevented from playing baseball, it may just be as simple as that.