I saw the show (matinee/evening) on Wednesday and was at the red carpet premiere on Saturday. I can't predict how big a deal this would be in the U.S. compared to Hamilton but I'm willing to bet it will be huge. There are a lot of U.S. fans of Harry Potter and the name alone draws sales more than Hamilton or LMM. The first sale for Cursed Child last October put me in an online queue of over 70,000 people trying to get tickets, with predictable aggravating technical difficulties. And that was more than 7 months before the show had even come out, before it had even been cast, much less reviewed. Much as I love Hamilton, there was not as much interest in that show when it premiered at the Public.
Cursed Child is not a perfect show but it is visually spectacular, with magic and spells occurring frequently, including things like Polyjuice transformations right in front of you (as in one actor on stage seamlessly transforming into another, without smoke or any other obscuring elements, which I'm guessing happens with the help of trap doors). I've read some of the script and it seems incredibly different to the experience of seeing it, and can understand why people are disappointed. But my point is, now that this has been given wide publicity in the form of the published book, and is now receiving very good reviews, the talk of and demand for this show will be enormous if/when it transfers to Broadway. Hamilton is big but a good majority of the U.S. population is literally oblivious to its existence. But most people know about Harry Potter, and the news of the show will spread even farther by the time plans to bring it to NY have been brought to fruition.
Hamilton Emotional Support Group:
https://www.facebook.com/groups/hamiltonsupport/