If we're going by who has the best records, then you open up a whole can of worms. I agree when you say that Cuba has a better record in recent decades than Russia, the US, and China. If you go back far enough though, even Cuba had violations. And if you go back even further (Batista), you're talking about out and out horrors.
Now of course, where does that stop? Because if we go back in US, Russian, and Chinese history the violations are out and out horrible as well. Some bordering on genocide. (I'm sure if you're a native American, you would say they were genocide.)
Point is, you can't always just throw the human rights violations of great powers into their faces all the time. The countries that are doing so well today in terms of respect for human rights, all had their problems in the past. They don't have problems today probably because they are not powers, let alone great powers. If we demand a spotless past, we'd end up with nothing but, like, eswatini or something. Politically speaking, you have to have the great powers on board.
Would it be better if these powers were not as openly hypocritical as they are? Yes, but that's just how the world works. A necessary evil in my opinion. The council would mean less than it does now if there was just eswatini or botswana or something sitting there saying, "You guys have violations."