Yes, kindness is incredibly exhausting. It requires you to consider the impact of what you say and do, and not just blindly forge ahead. Every single time you do or say something. It takes quite a bit of energy to do that, and just ignoring other people's emotions makes life much easier.
But dealing with an unkind person is also exhausting. And many people will, at some point, choose to not interact with that person unless absolutely necessary. That might be worth considering as well.
Does that mean you have to constantly agree with others? Not at all. But there are different ways of disagreement. One choice is "Well, you're wrong, and stupid, and here's my way". Another one is saying "I hear what you said, and I acknowledge you feel that way. But I'd like to point out there are things you might have missed". Sometimes, pointing out those missed items is the kindness.
Fake kindness - "I love everybody so much, and we all should just relax more" - is something you rightfully abhor. And I think you are right that it is a plaything of the privileged.
But concern for another person's wellbeing? I've experienced it from a wide gamut of people of all ages and classes. From a 3-year old sharing their cake, to a middle-aged manager taking hours to help me understand my career, to a 80-year old woman living on a meagre income, concerned people living next to her would feel welcome in the neighborhood.
If I could ask a favor of you, consider that kindness. Not the reshared Vonnegut quotes, but simply living with an awareness of others emotions. Not in deference to those emotions, but with respect for them.