The goal of a private space system is to have more money at the end of the process than you started out with, no matter who the customer is.

A public project is primarily concerned with filling the rice bowls of a great number of legislative districts, and if you end up in the hole, who cares? There's no real incentive for cost-cutting innovation, or spending less on the development and operation. This is true outside the space field, too.

You can tell exactly where NASA's space projects are built by who makes the most noise in their favor in Congress. There are both Democrats and Republicans in that number.

NASA is spending a lot less having private companies move their goods (and eventually people) than they would be either having the Russians do it, or building and flying the machinery themselves.

NASA isn't buying SpaceX components, assembling the rockets, or launching them. It didn't come up with the development money. It's paying for a service, and using less tax dollars than they would be otherwise. This leaves NASA more money to do other things.