They will and have. Look what happened to Larry Summers, Brendan Eich, or James Watson. In all cases issuing an apology didn't help them and lead directly to resignations. Heck look at the reaction of the University protestors to admissions of guild and apologies on the part of university administrators. Heck look who Christakis's apology failed to stop the events.

Ah. I see.

I'm not advocating an apology; that is playing the game according to the rules your opponents have set. I'm advocating -redefining- the game by changing what it is you have to apologize for. An example that is now recognized as such, and thus is no longer useful, is apologizing for the way what you said was received.