This assertion of causality is sorely lacking in accuracy. Your examples alone are sufficient for highlighting this.
Being among the most ‘government-run economy’ on earth at the time, the astounding innovation achieved within the Soviet Union is the most glaring contradiction. Cuba is just an awful case study subject, due to so many drastic incongruencies, but let’s remember technological innovation has been fairly low on Cuba’s priority list. If it weren’t their access to the world’s selection of material and media resources would have likely remained open. And this access was very obviously the reason they are driving old cars. Those are just two factors I will assert are far more useful in this sort of prediction.
While of course the correlation is circumstantially critical to varying degrees, many other measurements are better predictors of rich innovation environments.