I wish, but unfortuntaly the situation for these 2 shows are wildly different.
She Loves Me is produced by non-profit with different financial considerations from a commercial production. Live-Streaming this gorgeous production they put on also advertises Roundabout a whole, hopefully making people want to see their future shows, perhaps even buy into a subscription. She Loves Me has also been a financial success, making over 600k in recent weeks.
Bright Star on the other hand didn't make the producers/investors any money from their investment back, and on top of that them additional money every week of their run (except perhaps the last). How could they possibly justify spending more money on having it filmed?
We're lucky most producers budget the costs for a cast recording from the get-go these days, and we got that at least! Bright Star will live on though, I think it will go on tour and have a nice life in regional theater afterwards.
If we see more of these live streams it will be, like many other people have said, be from limited runs of non-profit productions like Roundabout and perhaps Lincoln Center.