I agree with you about the essential importance of education and a strong economy. I also agree with you that China see space achievements as a good way (among many) to express its desire for leadership.
But China lags significantly behind the U.S. in areas of education, economy, and freedom of expression. The latter is important because it is an essential ingredient for long-term innovation.
I think we'll see China do some great things in the near term, perhaps even put people back on the moon. Americans will be freaked if that happens. (I'm sad to say--I wish people would take a broader view of humanity, but oh well.)
But in the long run I think we'll be doing big things in space too. It just looks shitty now because we're between big launch systems.