The only reason China isn’t dominating is because of SpaceX. NASA helping fund flights is great and helpful to SpaceX but don’t mistakenly credit NASA for SpaceX’s success.
There's a tendency by some to describe money paid out by the government for services rendered as "government funding", framed like some sort of unearned charitable gift given by the government to the company which entitles the government to all of the credit in the end. This is an immature point of view that is often the product of motivated reasoning (particularly, motivated by personal dislike of the people/companies involved. There's also some people who thought that capitalism would be trapped on earth with space being the exclusive domain of governments, and are bitter to realize that won't be the case.) Maybe your comment is reacting in part to this tendency, I find myself frustrated with it as well.
Nevertheless, the truth is that SpaceX didn't have the money to develop Falcon 9 until they got that contract. I think themgt is correct to say the creation of contracts like that in Europe could provide European rocket companies the same kind of opportunity to develop technology and prove themselves.
Europe has literally just spend 5 billion $ on a SINGLE rocket. Its not hard to understand why they don't have money for anything else.
SpaceX was saved by COTS because they were able to borrow money against that contract. And it really only included a couple 100 million to develop the initial Falcon 9. The waste majority of the money was for Dragon.
And they could do it that cheaply and fast because they had the legacy of the Falcon 1 and its infrastructure to build off. And that was mostly developed privately.
At the end of the day SpaceX underbid on COTS and actually didn't make money, it only helped them develop things that would make money other ways.