I see him not only as mediator between people and feelings now, that I see him as a mediator at all

but even more as a mediator between people and their feelings (and himself and his feelings) and the world around. He gives feelings some grounding and the conscious base they can act on, I think.
As seeing queens as teaching and kings not, I think that's maybe really a little narrow, Elentir, but I think you maybe just didn't tell us all you think, afraid of another really long post

- I think they both Kings and Queens have the same lesson to teach, that of their suit, but they do it by different means. The Queen teaches us by her example, we see the way she is and follow her there. She may even explain it, but she's the principle itself we may follow or not. The King demands obedience to his laws and enforces it, if necessary. He teaches more from the book, more from his brain. He's the worldly ambassador of Hierophant and Emperor where the Queen brings Empress and High Priestess into our world, to some extent.
At least, that's the way I see it.
Your comparison of King of Cups vs. King of Sowrds makes me post that one next, it's too good