Gendry took up the banner of his royal birth on the wrong side of the blanket, eagerly. He knows what it's like to be common as does Davos. Davos though is very much into making sure he's a top adviser to a king, any king. Davos went shopping for both Jon and Gendry. Varys also knows common life, as does Melisandre. But as she said, they aren't common any more. Arya actually showed a concerned for common people, not just being about the butcher's boy. But in her service as a Faceless Man. But she has explicitly rejected that.
The only characters to consistently *do* things for common people are Daenerys and Jon.