In some ways, it might work better as a film because while I really liked the stage show, it drags a bit during the second act. Animation or a highly stylized approach could work.
What the stage show does very well is immerse the audience in the world of the musical. That's why it almost always seems like a shadow of itself on television, with the odd exception being the performance on the CBS Sunday morning show of "Wait for Me II" thanks in large part to Eva Noblezada.
So the challenge of filming the stage production would be to capture it in compelling fashion. One reason I'm definitely in favor is to preserve the performances of the wonderful cast. Andre De Shields probably wouldn't be quite as compelling onscreen as he was in the theater, where he captures the audience with the slightest movement, but I'd love to see it preserved in all its glory.