I agree with most of what you said,but Dana Carvey did do a funny,but perhaps not very accurate,imitation of former President Bush.
Their political stuff has generally been pretty good. I remember one bit with Reagan playing the gentle geezer to a boy scout troop, then barking out orders and speaking in Russian to the Soviet Premier on the red phone as soon as the scouts were ushered out of the room. Hilarious.
"Strategery" was a SNL invention, and then Bush coming up with "dignitude" when he and Gore were playing Scrabble.