Ariane Space is private, too.
United Launch Alliance is also private.
I think there are many reasons for the current situation.
First, Space X has a grand vision and is driven by it.
They have excellent management and ingenious engineers.
Second, (IMHO) Obama's economic policies included picking winners.
Space X got a juicy contract for many, many missions.
The US is buying US first, so Space X has a nice base-line launch volume that enables them to go towards "mass"-manufacturing.
As a result, cheaper prices drive demand even higher, increase volume, and lower prices.
The US government has a more innovative approach to industry policies than the EU.
This brings me to the third point: what the EU is doing wrong. While the US tends to _buy the product_ of the new industry they want to create, the EU _funds the research_. This leads to the current situation in which Europe, which had a lead in methane engine research[1], has no methane engine, while the US has a company that earns money by launching a reusable methane engine.
Point four applies to the US and EU: While Ariane Space is private, the money comes from the EU and the partner countries (mainly Germany and France). Engineers did not design Ariane 6; it was created by politicians who squabbled about where which part would be developed and manufactured. There were two competing plans, one driven by Germany and one by France, based on which country would benefit more.
I'm unsure about ULA, but at least SLS had the same problem.
So, in Europe, government funding comes with strings attached, and it goes towards research. People laugh about the CEO of Ariane (rightfully so for other reasons) when he complains that Europe is not buying enough launches from them to justify reusability. But he is right on this one. A rocket company needs a baseline of demand to justify going into "mass"-production and reusability. _After_ that, the lower prices will create new demand. In my opinion, this is how it worked for Space X and what Europe failed to see.
In my opinion, both Tesla and Space X are good examples of how to establish new industries (from the view of the government):
* find a private entity with a grand vision
* buy their product
* use economics of scale to drive down prices
The EU has started incorporating some of these ideas in its latest round of research funding.
[1] I don't have hard evidence for this other than that one of the researchers told me. Even if Europe didn't have the lead, we had cutting-edge research.