Using Konjunktiv II and/or modal particles is not about politeness but about changing the tone in general. Both methods are used frequently.
Konjunktiv II adds a counterfactual tone: We aren't talking real, okay? This can be polite in some situations. In others, it can be impolite or neutral.
Ich weiß, was zu tun ist.
Either We have to do it this way! or more likely as an irritated answer: Your advice was uncalled-for.
Ich weiß wohl, was zu tun ist.
I know what I'm doing. (Your advice was uncalled-for.)
Ich wüsste, was zu tun wäre.
May I give advice?
Ich wüsste wohl, was zu tun wäre.
Please take my advice.
Eine Frage habe/hätte ich (doch) (noch).
Hätte sounds just a tiny bit more smarmy. Adding doch adds the meaning that's my only question. Adding noch adds the meaning that's another question. Adding both is an excuse you came back to ask another question though you used doch last time already.
Diese Sache haben/hätten wir (also) geregelt.
Both hätten and the particle also express relief about coming to a conclusion.
Da ist/wäre er (nun) aufgewacht.
Both wäre and nun express deadpan notice about the late awakening.
Impolite Konjunktiv II phrase:
Hast du das nicht machen können?
This is just a question about facts.
Hättest du das nicht (mal) machen können?
This is a very rude prompt to be courteous.
The key is the combination of Konjunktiv II and the modal verb können. You could do something, but it's a counterfact. You did not. And I'm angry about it.