I think what you might be describing is that scarcity as necessary but not sufficient condition. Question then would be, other than Bitcoin, are there in the world scarce things that nobody wants? Or I am wrong, and all scarce things are desired by humans, and thus have value?

I agree. Humans seem to have a desire for scarce things, but this can be outweighed by a difficulty or burden of possession, or perhaps it's something offensive to human nature. So, yes, scarcity not sufficient in all cases, but in conjunction with bitcoin's other properties, probably its most powerful.