If the private sector model of an economy is worse, then why has every first-world country begun to follow it? Because it's more effective.
You can argue that the private sector is a different tool for a different sort of job, but my point is that regardless of the job, small organizations almost always do it better. (Incidentally, that's the thesis of startup investing.)
The exception is with highly parallelizable tasks, like fighting a war. But space exploration isn't that sort of job.
I feel like I'm in an alternate universe. Strange day. It seems like it should be perfectly obvious that private sector control is more effective than public sector control in almost every area where people need to accomplish things. There is practically a mountain of evidence in support of this viewpoint, and it's hard to find examples that contradict it, unless it's also a highly parallelizable task like constructing a highway system. The most obvious counterexamples that come to mind are the justice system and monetary regulation. But those are two counterexamples in a sea of examples.