I would say purely "because it works". SpaceX has received a ton of funding, for sure. But they've delivered incredible advancements in reusable rocketry, methalox fuel cycles, cost to orbit and much more, while SLS was literally a flying scrap pile that was late and over budget despite being reused 1980s tech.

Let's not pretend that NASA rockets were really public work either, with most of the development and construction done by contractors like Boeing, Lockheed Martin, Aerojet Rocketdyne and more... But these old guard companies were happy to keep turning out the same old product with incremental improvements.

SpaceX could have been a tremendous failure or success with the risks they've taken, and we're all lucky it turned out to be a success (so far...). It says it all when they are going to launch Orion on SLS but Starship is going to be waiting there at the moon for them. Well, if it doesn't blow up on the pad.

The space program of every nation have always worked that way. Even the Soviets were using Rhode Schwarz made gyroscopes. The Apollo rockets were built by the private sector.

The only real difference now is the ferrying contracts.