This isn't about cost, it's about privatizing space the same way the internet was privatized. Take technology developed in the public sector and allow the private sector to take it.
With the privatization of space, you will get both the same upsides and downsides of privatization.
The only difference between the past, where NASA paid private contractors to build Apollo and the Shuttle is now they are paying a private contractor (SpaceX) but SpaceX gets to sell the tech for others to use besides the government.