The main takeaway is that it really didn't matter what you said or how you said it.
Then you were simply using skill challenges incorrectly. Both of those things should always matter when running a skill challenge. A wisely-chosen turn of phrase or clever action should earn a success without rolling; a truly self-sabotaging action should earn a failure without rolling. The state of play should change from one action to the next, that's the whole point of having initiative involved. As others have said, there may even be cases where a particularly clever/foolish or complete response just ends the challenge one way or the other; this should be rare but hardly impossible.
No wonder you hate skill challenges so much.
It doesn't take several pages to explain skill challenges in an effective and productive way. I could easily do it in just two. (Not counting space eaten up by art or things like tables of difficulty values or the like, of course.)
"the only way to win is to ruthlessly crush your opponent" is absolutely a political statement.
Okay. Is that somehow
advocating that people do that thing? Because that's very clearly the point you want to make: having political content of any kind is
endorsement of certain kinds of behavior. Does that mean having dating mechanics in a game is endorsement of cheating, since players can cheat on their SOs? Does that mean D&D endorses violence because the vast majority of its rules are about how to make others die in violent combat?
The core point does not hold. A game where you play a ruthless, scheming noble cannot be equivalent to saying that assassination is a good and noble thing that people should totally do. The very notion is ludicrous.
(Also, "the only way to win is to ruthlessly crush your opponent" is not actually true of Coup. You can also win by simply
outlasting your enemies. It is more difficult, to be sure, but if you play the long game and simply
survive long enough, you can win by buying off those who support your rivals, until you are the only one left with supporters. It's a risky strategy, since assassination is an available tactic in play, but luck and skill might get you through. Much of your ability to win will rest on your poker face and your ability to see through others' deceptions, as the best "honest" ways to strip someone of their support are to successfully challenge a lie and to prove that you did
not lie when challenged.)