I think this is making too strong of a claim based on fairly simplistic arguments. I'd find this whole argument more convincing if instead of the overarching and fairly "fuzzy" label of democracy, if there were more specific traits. I suppose that the more nuanced (and less pithy) version of your argument might be that "the higher a country rates on Freedom and Prosperity Indexes, the less likely it is to have problems A, B, and C."

I'm sorry for being the annoying pedant, but remember that correlation is not causation. Reality is messy and complicated, and while the narrative of "freedom causes wealth" is appealing in it's simplicity, there are many other factors that impact wealth, happiness, and lack of problems.

There is no extreme poverty or starvation in democratic countries

This seems like a strong claim to me. What's your source for that?

and access to education and health care is one hundred percent, at least in older democracies. Younger ones are getting there fast.

Where do you draw the line between older and younger democracies? Isn't the US pretty old compared to other democracies [1] - and does it provide "100% access to health care" to its citizens?

all countries and all people lived in democracies the major problems of humanity would be solved or be dramatically smaller.

Would you classify X-Risks like AI and pandemics as major problems? Do you think having more countries be democratic would reduce these risks - given that the existing democracies don't do enough on either?

[1] https://www.weforum.org/agenda/2019/08/countries-are-the-worlds-oldest-democracies