I’d like to add one more general observation to these [Koellner's] compelling remarks. In cases like this one, where the evidence is overwhelmingly extrinsic, there’s no reason to expect the relevant discussions to be ‘generally understandable’. It’s only in cases like the HP, where the evidence is intended to be primarily or even exclusively intrinsic, that ‘general understandability’ becomes crucial. (If the principles are supposed to follow from the concept of set, then we need to be able to see how that works.)
PS to Peter: Thank you very much for your message and slides about the current state of understanding on choiceless cardinals! I look forward to spending a bit more time with them both.