How would they bring stability? The main reason if instability is that there is no approximation of how much Bitcoin should really be worth. So when it goes up or down by 10-20%, the market doesn't know if it's a good opportunity to buy/sell, or if the movement was justified. If institutions merely hold Bitcoin and don't actively trade it in a way that would stabilize the price, then they would have no effect. But they might as well be destabilizing Bitcoin by amplifying the existing price movements.