People can put up with a sleazy politician but they can't live comfortably knowing they can't trust their neighbors or trust the police to fight crime for them when the police know DAs will reduce charges, drop charges, etc. Like why bother putting in hard work where you're putting your wellbeing in the balance just so that criminals go unpunished... eventually you end up with a "Caracas" & wild-west experience.
Quite to the contrary, when we observe rampant cheating from the presidency down to shrinkflating food and freeriding the subway, it is a good argument for having an universal morality problem.
There isn't a dichotomy between the saintly people and the scummy political class. A nontrivial part of the voter base of the scummy politicians is formed by regular scummy voters.