Put hold on your optimism.
Launch vehicles make only a minor part of the whole space programme, invariably of whether it is privately or publicly run.
Rockets are an industry with financial model not unlike latest generation microelectronics, or jet engines. It may sound surprising, but just look at digits.
It is also very similar in that regard, that it is near impossible for a newcomer to kickstart a business. You can be nearly 99% sure that there will be no company that will deliver GE9X competitor tomorrow in case of jet engines, or 7HPC process in case of semiconductor. The "added value" (really hate the term) on top of the basic piece of metal is many many times bigger than its material value.
In that regard, the Soyuz being still relatively cheap, and being launched by regular engineers, rather than by 1000+ people with postdocs is a real advantage.
My own prognosis is that China will eventually take lead in small payloads with cheap as dirt solid fuel LVs. And for anything else, it will still be a niche for nation-state backed heavy launcher programs.