Does any other industry remain shuttered? Why shouldn't Broadway attempt to reopen - as you stated, when does it end? We now have a vaccine that keeps the majority safe (yes, even with Delta - the news of breakthrough infections has been widely exaggerated over the past week) - what more should they wait for?
People are going to indoor museums, flying on planes, going to amusement parks, going out to eat, all with children and many in places that don't require masks and have higher COVID and lower vaccination numbers than NYC. The Broadway League and NYC have laid out a plan which requires vaccination and masks. I have yet to take my un-vaccinated children to an indoor restaurant, but will happily take them to the theater in September under these conditions.