I used to think about that as well, when I watched the show during its original run. I don't watch the reruns.

(And I guess I should say at this point that I'm not black.)

But I saw the show mainly as a positive for black people because it went against type. It showed a black doctor, it showed black kids going to college and excelling, it showed black people in a nice house in a nuclear family.

Another thing it showed was the variety of different "looks" that qualify as African-American. The oldest daughter, as I recall, is a person who easily could have "passed" for white. I also remember being surprised at hearing what sounded like a "white Southern accent" from one of the black female students at the college where another Huxtable daughter went to school.

The show told me that African-Americans come in many different hues and have many different voices.

On the other hand, I understand the criticism that perhaps by taking a daughter who "looked white" they thought they were making the show more palatable to a white audience.

Watching the show also reminded me of what was once said of families in 1950s sitcoms. Someone did a study that showed that if you priced the homes, furniture and other possessions of families in such shows as "Ozzie and Harriet" or "Leave it to Beaver," you'd find that the families were living major upper middle class lives.
I think the Huxtables qualfied for that distinction as well.
To live the way they did, with five (?) kids, college tuition and a big house, they had to have been pulling in $150,000 a year, based on the cost of living at that time.