Connotations aren't universal. I think "pure" or even "authority" could be argued to have positive connotations in certain contexts and to certain people.
> fairness and caring for others have zero negative connotations
Nobody has ever accused another of letting sentimentality or "heartstring stuff" interfere with long-term/greater good? A whole lot of "law and order" or "pure reason" types from time immemorial stand as counterexamples.
> purity and authority have many negative connotations
Also many positive ones. You think evangelicals don't prize purity above some of these other values? You think all the "strong leader" rhetoric doesn't play on people placing authority pretty high in the moral pecking order? Are people evil for being amenable to those manipulations? Who's demonizing now?
What you perceive as positive or negative connotations reflects your beliefs. Don't attack others for what you put there.
those are universally respected and well received attributes across time, culture, and space.
purity and authority have many negative connotations. I don't even need to say them.
I feel like it's disingenuous of you to claim otherwise.