They could sell the shows many times over and keep selling it after the run has ended. I have never been able to fathom why they haven't done this. Yes, I know there would be issues, but they would be easily worked out.
For theater, there's a fear that recorded availability will hurt the... sorry, my brain is struggling for words today... desirability / exclusivity... Reducing the scarcity and prestige of Broadway tickets will reduce the demand, lower overall ticket prices, and make high-end patronage by the rich less desirable. Producing live theater is more than just ticket sales. There's an element that's similar to high fashion, the diamond industry, and other industries with artificial scarcity and manufactured hype.
Aside from the image issue, there's also a fear that home media will hurt in-person attendance to the point that the performance is impacted. Live theater is impacted by the audience. A full house of responsive people is dramatically different than a sparse crowd, both for the audience experience and the actor's performance. Even if the VR quality is amazing, the whole thing dies without an audience. The most technically amazing capture rig can't give a live theater experience if the rest of the seats are empty. Even putting in a fake crowd wouldn't fix that, since the performance would be different.
It's arguable if a home theater is better or worse than a cinema for a motion picture, something pre-recorded. Yeah, being in a packed theater is different than being at home, but some people might prefer the quiet to watch a movie. The film is still going to be the same, either way you watch it. No amount of audience laughter, gasps, applause, or any other reaction is going to change what comes out of the projector. That's not true of live theater. Seeing a show on a dead night is not the same as seeing it with the seats full of lively people, and it's not the same performing under those different conditions either, even when the fourth wall remains unbroken.
I'd like to think that the fears of wider availability through recorded media hurting in-person attendance are unfounded. It would be great if making Broadway more accessible could increase live theater's popularity. Ideally it would spark interest in people attending local theater productions in-person, in addition to drawing more attention to the big leagues. However, I don't think anyone really knows for certain what the end result would be. For an industry that's continually struggled with all sorts of perception issues, I think it's understandable that it's been difficult to get them to accept a change that has the potential to kill off their art form.
That's not even getting into licensing, royalties, residuals, negotiations with unions, and all the other stuff that has to go on about who gets paid, for what, and how.