Out-of-universe, Roddenberry wanted the cast of the Enterprise to reflect his dream of what the Earth of the future would be. Therefore, the social commentary of having Africans, Asians, and Caucasians serving together and working together peacefully outweighed the need to be accurate about what a post-racial Earth might look like.
In-universe, even if racial tensions disappeared over night, it's possible that racial differences could persist for much, much longer. Studies have should that people tend to be attracted to people who look like them (or their parents). In short, even while being completely tolerant and accepting, people may end up dating people of their race for perfectly benign reasons, causing racial differences to persist.
Also, multiple characters in the Trek universe show strong pride for the cultures they were raised in. Sisko is a Creole-cooking, baseball-loving African-American from New Orleans. Keiko engages in several Japanese traditions, and works it into her wedding. Chekov freakin' never shuts up about the fact that he's from Russia, and parrots old Soviet lines about how Russians invented everything. To say nothing of the entire colony of Native-Americans who are still practicing their traditions, and moved to an entirely different planet to do so.
All of which is a long-winded way of saying that the Trek universe isn't a homogeneous society, it's an extremely tolerant one. Differences are acknowledged and celebrated, and no one judges or discriminates against those of different cultures. I don't think that it's surprising that within that society, people still tend to marry and gravitate towards people of similar races and backgrounds, while not holding any sort of animus towards people who are different. But for every Ben and Jennifer Sisko, there's also a Miles and Keiko O'Brien.
Also, while it's true that Trek doesn't show many multiracial officers, it does show a lot of multi-species officers. That's gotta be more impressive, right?