Well first of all, money. Airing it, lugging production equipment around, more labor. More road agents and longer preparation.
House shows are used as practice for numerous things. An appeal of a live event is that it is not on TV. You have to go to it to see it (as Yaz pointed out).
Not a good idea here.
The Rock proposing to his Girlfriend
Rock: Will you marry me?
Rock: IT DOESN'T MATTER