I'm not sure that I understand this play. The "its misogynistic" diatribes don't really grapple with it in an effective way. They founder on the fact that "shrew" is a relatively nice label to put on Katherine. She does tie up and beat her sister after all. The dialogue is crackling and it is clearly broad farce that is meant to be played fast. It reminds me a little of the screwball comedies of the 30s and 40s.
The whole thing is very complex, as Shakespeare always is, and it is not helped along by the commentaries on it being so simple minded. I think that I will have to read this play several times or see it played a few times to understand it. There are a lot of weird interlinking bits between the Katherine romance and the Bianca romance. There is a weird interplay here between farce and Shakespeare's psychological realism.
I have a certain tendency to think of it as a romance between two crazy people plus Bianca's courtship.
I don't think that anyone understands this play. Shakespeare did not understand this play, the ironic staged re-interpreters do not understand this play, the academics do not understand this play and I certainly don't understand it.