I think a lot of it has to do with tone and medium. Cursed Child is very much something written to be performed on stage and not read like a book. (And IMO this is a big reason why the Fantastic Beasts movies have been such a mess - they're not written tailored to the medium they are.)

For example, I went in knowing some of the criticisms and stuff like the Ron/Hermione storylines/interactions (which I know were received poorly by readers) absolutely killed on stage because it came down to the actors performances and how it was staged. It was more lighthearted and (save for a handful of moments) didn't take itself all that seriously.