Innovation thrives on the rule of law, independent courts and neutral arbiters of contracts, habeas corpus and due process, the right to a lawyer, and the right to uncoerced testimony.
Consider Jethro Tull, the farmer. In 1700 he was 26 and he was taking over the family farm. He hired some local hands to seed the fields that spring. As had happened for thousands of years, the workers took bags of seed and cast handfuls on the ground. Jethro Tull became angry, because there were patches of ground that had too much seed, and other patches of ground that had too little seed. He went over to the workers and asked them to be more careful. But they proceeded as before. Tull became more angry, and went to speak with them again. But they still ignored him, and kept doing their work in the traditional manner, as they had since they were children, and as had their parents before them, and their parents before that. Tull was in a rage, but saw he could not change how the workers did their work. Instead, he decided to build a machine that would plant seeds at regular intervals. This was the beginning of the Agricultural Revolution.
https://en.wikipedia.org/wiki/Jethro_Tull_(agriculturist)
But now ask, why did this happen in 1700, and not in 1680 or 1660 or 1500, for that matter? Was Tull simply smarter than any farmer that had ever lived before that time? Or was their a new legal system on his side?
In the time of Tull's father, England was still burning witches. The last great spasm of irrational fear and witch burning swept over Britain in the mid 1600s. But then Britain passed the Bill Of Rights, in 1688. Now everyone had the right to a fair trial, and a right to a lawyer, and no one could be tortured into confessing to a crime, such as witchcraft. And Tull belonged to the first generation of entrepreneurs in history knowing that they could depend on the rule of law -- the government could not take arbitrary action against him, but was constrained by its own processes. Therefore Tull could shatter tradition, and do completely new things, without the threat of being burned as a witch.
I could cite an endless number of examples. Galileo made brilliant discoveries in an illiberal nation, and was put under house arrest, Newtown made discoveries in a nation of laws, and he became a national hero. Simply knowing that laws will be enforced fairly defeats a lot of the kinds of evil scheming that spring up under authoritarian regimes.
"Freedom" is an empty word. When talking about the kinds of environments that cultivate innovation, it's best to try to be specific about that environment. History teach us the raw ingredients: the rule of law, fair and independent courts, habeas corpus and due process, the right to a lawyer, the right to uncoerced testimony.