@kgw The thing is, the Supreme Court is intentionally powerless in the US system. It was by intention that executive powers were kept away from that branch of government, and so the Supreme Court really only has the influence that we ourselves project onto it.
So it's an interesting question, I don't understand how a Supreme Court can be as influential as it is? Well that's because the person asking the question is subscribing to the idea that it is influential.
Otherwise, the Supreme Court can write whatever opinions they want, and they will land like a stone and go nowhere.
Unless people decide to recognize those opinions as influential.