What exactly is unhealthy about more atheistic societies? By measurements such as the Human Development Index, there's actually a very clear correlation with more religiosity and worse quality of life, which could imply that religion worsens quality of life (should be obvious in many countries like Afghanistan), and/or that those with poor quality of life seek religion, and/or various underlying factors. But I don't see any way to argue that a lack of theism, deism, etc, worsens society, when all the evidence points the other way: https://whyevolutionistrue.wordpress.com/2012/05/13/the-correlation-between-religiosity-and-well-being-among-u-s-states/
IMO that evidence is bogus. The south has been doing shitty economywise ever since the civil war. At that time the north was just as religious, but not dependent on slave labour, cotton and other outdated sources of wealth.
The West achieved dominance in the world when atheism didn't even exist yet. And it persists to this day.. why? I don't think anyone really knows.
I also don't think you should measure a society's 'health' by means of the HDI, as it only measures three criteria: life expectancy, education & income. And these three are all intertwined. If you got the money there's no problem organizing decent healthcare & education. Without money.... it's an unachievable goal.
The real health of a society is hard to measure, as it encompasses immaterial factors such as 'citizenship', 'responsibility', 'self-confidence', 'ambition', 'philosophical views' (optimism vs pessimism or nihilism), etcetera.
And judging by these values I imagine the west not doing so well anymore. They may be rich, but they owe it almost entirely to the generations that came before them. They lack the inner drive of the people that live in the upcoming economies. The people in East Asia & Eastern Europe work much harder, don't dwell in decadent nihilism, but are proud of who they are and know what they are working to achieve. That makes their societies more healthy than ours IMO.. there's much more potential there and it will only be a matter of time before they have gathered enough wealth to set up supreme health care & education.
But unfortunately for them, they too define their goal merely in material terms. So they are likely to end up at the same place as us.
If a nation (or empire) wishes to maintain its dominance it's vital not only to hold onto its economic & political dominance, but also to maintain its 'spiritual' drive.
The failure to do so is IMO one of the most important reasons for the collapse of the Roman Empire, as well as it is for the "downfall" of the US in modern times. The sense of mission that drove the Americans is quickly being replaced by a general feeling of doubt and apprehension. I'm pretty sure people in the future will consider the Iraqi affair as the death sentence of US supremacy, not because there they encountered the boundaries of their might, but solely because they lost faith in the validity of the American mission worldwide to bring freedom & democracy to people supposedly eagerly craving for it.
We're becoming less religious for sure, but nearly 100% of our politicians are religious; you can barely even run for office if you're not a Christian.
As much as it may hurt your atheist heart.. I wouldn't complain about it. God is one of the major pillars of American society, if you break it down you will surely hurt the moral fabric of society, and thereby, society itself.