The US space program has always been privatized. The Mercury program was McDonald Douglas, Apollo program was Boeing, and the Space Shuttle program was Rockwell. Said companies weren't just the prime contractors responsible for design and manufacturing but also contracted for launch operations.

NASA space launch has always been contractors all the way down. The only thing that changed over the last couple decades is were the liability lies. The previous system of NASA being responsible for all the failure, held hostage by contractors, wasn't sustainable and under the Obama administration an initiative was launched to restructure things so all liability was on the prime contractor for any program. The old system was NASA contracting for labor and the prime contractor giving it their best effort rather than NASA contracting for a finished product. NASA now buys a finished product, a commercial relationship, rather than signing contracts for design services, manufacture, and launch operations that have no contractual guarantee the product will actually be delivered. This is why Boeing has actually lost money on the Starliner and SLS program rather than the previous situation of being able to hold NASA hostage milking more money as a reward for fking up.

Another fun fact is the US National Labs are also privatized and have been since the very beginning. National Lab scientists aren't even US government employees and their salaries come from whatever corporation has hired them to work at the lab. The US government owns the real estate and issues grants for the research to be done but the labs themselves are private sector operations, each one operated by a handful of corporations. It's why the US government never owns the patents from US national lab research.