The fact that Cosby's rape allegations were the lead headlines on every evening newscast is testament to the Cosby Show's impact.
Those allegations have been around for years, but Cliff Huxtable's persona was so powerful that people actually conflated Cosby with his character. Took a full 3 decades for people to separate them. And some STILL don't. And you better believe when Cosby dies much of the animosity will go away (not saying it's right, but it's the truth).
And if we really want to be petty, Cosby was so popular that it generated a very successful spinoff in A Different World. Joey on the other hand...