NTlive stats are all I’ve seen. In 2015 they spent £5.1m and earned £6m and 2016 spent £4.4m to earn £5.3m. I’m guessing the second number is actual profit but it could be the difference is actual profit which isn’t much for a worldwide distribution. And London film costs are
£300 compared to US film cost of $2-4m. If those numbers are correct, then shows like bandstand and allegiance probably lost money in filming while London shows like 42nd street and Billy Elliot were profitable. It’s probably why American in Paris was filmed in London.
So I don’t see a lot of change in broadway filming. But regional theaters cost are probably substantially less and might have less issues and exposure of subscription season might outweigh any loss in streaming.