Maybe the combination of capitalism + democracy is so successful because it aligns the incentives of leaders and the masses best (to the extent possible).

I think not. European colonialism was hardly a democratic project, and the extreme success of the US is attributable less to ideology and more to being an entire continent with a relatively tiny indigenous population that had not exploited any of its natural resources. Ideological/paradigmatic competition is not some neat controlled experiment where you can normalize existing conditions to unity and then draw conclusions from measuring subsequent growth; initial resource distributions make a massive difference and geography, while not the only factor, is highly determinative.

My takeaway from China is democracy is less important than political competition. Between Mao and Xi, the CCP had the latter without the former. Today, America has the former and is struggling to keep the latter.