Even though many of the libels thrown at JKR are eminently winnable, people such as scientists, doctors, and even judges, lose their reason when it comes to this issue and feel they ought to decide things on a very mistaken view of what's been going on and what public opinion is.
This is the kind of case you need to win at first instance. For JKR winning at appeal a couple of years after losing in the High Court and being "publicly declared a transphobe by the English legal system" would be a disaster. The first decision would be the one remembered and forever discussed.
However, even if the lawyers were sure a case could be won, it needs to be won against the right defendant. With anyone too small there's a risk of things going a bit McLibel, even with a win. It would need to be carefully managed not to look like a hugely wealthy person using their wealth to destroy plucky under-dogs defending the most oppressed ever™.