That does not prove causation. The reason why these countries, such as France, Sweden, the USA etc. grew so rich is because they once subscribe to laissez-faire capitalism.
No, it's because they allow markets to develop at the same time as they set up social services to ensure a basic standard of life and some level of social mobility. They aren't mutually exclusive. This is what I keep saying. No one is suggesting that markets be ELIMINATED (maybe some people are, but I'm not), what I'm saying is that these societies decided that they would essentially create a baseline. Every person gets a certain amount of education, and everyone gets decent health care, paid for through taxes, and this was decided through the democratic system, which the people own. It has resulted in a higher quality of life, a more educated and healthy population, and a healthier democracy.
Do you think a poor African nation could on it's own institute health care and education (to the degree their governments are able) and they would magically become rich?
Well to some extent the governments of African countries could use their resources more wisely and education and basic health services would be a step along the road to creating a robust economy. I don't think the only path to a developed economy is through vast inequality of wealth, the extreme poverty of some, and the extreme wealth of others.
Yet Botswana instituted limited government and it was the worlds fastest growing economy for 50 years.
And China freed up their markets, which resulted in the improvement of the lives of millions of people. There's no question that market-friendly policies and market liberalization have their place in the toolbox of policy, but it's dogmatic and untrue to suggest that any form of government involvement is negative. Finland's educational system alone proves this, as to the NHS's of Canada and the UK, etc.