If we’re measuring by economics then whether it’s a democracy or some flavor of authoritarianism matters a LOT less than how corrupt it is. There can be reasonably non-corrupt autocracies and there can be horrendously corrupt democracies. And how corrupt a government of whatever form is often has more to do with the multi-century culture of the place than it does with the form of government du jour. That’s “often”, not “always”.
Here’s another way to view the problem.
The populace of a country that’s both poor and under autocratic rule probably wants their country to become both middle-class-to-rich and also democratic. So which problem does the public at large try to fix first? And in countries where “civil society” is weak and the public is largely powerless short of a spontaneous mass uprising, which problem is more likely to be addressed first by the autocratic government for its own ends?
I will suggest that whether it’s led from the bottom or the top, addressing the economy and the total wealth in society will be tackled first.
In places with dead (more like killed-off) civil society, economics is the one and only outlet of the masses. Whether they’re moving from subsistence farming to urban pushcart salesmen or from pushcart to tin shack or from tin shack to rented mall space, it’s the allure of economic security and the power of human labor that will move the economy forward. Meantime, the local fatcats, even if they’re pretty minor players compared to more wealthy countries will have the same desires, just on a different scale. And yes, they can often harness the autocratic government to help them deprive the lower classes of much of the fruits of their labors. But large or small, part of the government or not, they’re all trying to get rich(er).
Right now between, say, WWII and 2100 a vast slice of the world is embarked on the “get rich now” program. Will they arrive at the “get democracy later” place? Some already have. E.g. South Korea. Some are a work in progress now. E.g. eastern Europe. Some may never, e.g. Afghanistan, Russia.
The rest will each have their opportunity at some point unless something else intervenes first. Be that economic catastrophe, global warming / sea level rise, hostile invasion, pandemic disease, a very deeply rooted kleptocracy taking hold, etc.
Democracy really is a luxury of the socially secure and the economically comfortable. For those people and countries born into that circumstance democracy feels kinda like air and gravity; it’s just there for free in inexhaustible supply ready to be used by everyone everywhere for everything. That’s far from a realistic appraisal of the actual situation though.