Journalists don’t seem to know how to report on politics when people are not acting in good faith

This is exactly it. They either don’t know how to react to it or they simply refuse to acknowledge it out of fear of jeopardizing their disingenuous absolute neutrality facade.

Why assume that Republicans stated motivations are genuine at this point?

Literally no good reason.

Republicans know that they will always be given the benefit of the doubt by the media and that their radical messages will be transmitted directly to their supporters and then sanitized and normalized when repeated by other media outlets.

Yup!

Sartre described their bad faith perfectly when he talked about antisemites:

“Never believe that anti-Semites are completely unaware of the absurdity of their replies. They know that their remarks are frivolous, open to challenge. But they are amusing themselves, for it is their adversary who is obliged to use words responsibly, since he believes in words. The anti-Semites have the right to play. They even like to play with discourse for, by giving ridiculous reasons, they discredit the seriousness of their interlocutors. They delight in acting in bad faith, since they seek not to persuade by sound argument but to intimidate and disconcert. If you press them too closely, they will abruptly fall silent, loftily indicating by some phrase that the time for argument is past.”