You can’t disprove something like that. You can make convincing arguments, but only to people that don’t really believe in the first place; it’s just arguments if their faith is good.
Seriously, you can’t prove an invisible, undetectable phenomenon doesn’t exist. You can only prove that it doesn’t give any measurable affects. And that’s measurable so you just go right back to arguing to a wall if the faith is there.
But, no, the rest of the premise is flawed too. There are plenty of secular humanists that aren’t depressed, and plenty of people in religions, including christianity (since that’s the bias the question has) are.
Besides, who says the idea of an afterlife is comforting? Or that any given afterlife would be if you accept all of them as possible? The idea is absolutely horrifying to some because you’re stuck with whatever it is forever. Eternity, stuck in some religion’s heaven or hell, and neither is exactly as rosy an outlook as you’d think before looking into what is canonical about the various heavens.
But even reincarnation is horrifying. Doing this shit over and over and over until you get lucky and get the right life to figure out how to escape the cycle? Fuck that noise.
Joining a universal consciousness? Just as bad. Stuck in that state, watching the horrors of the universe play out? Not even if I don’t have to remember being human, tyvm.
Life was absolutely not better when christianity was even more dominant and using whatever sick ideology of the afterlife they cooked up as a threat to obey.
Hell, just the idea that people weren’t just as depressed 100 years ago is bullshit. They just didn’t talk about it. But I had the opportunity to sit with people born in the 19th century, and can tell you that faith in an afterlife did not make them less depressed. It may have, on an individual level, helped them process grief, but that’s a different thing, and I can promise you that nothing tests faith like grief.
If depression is more common now (rather than being more reported and discussed, and I don’t know which it might be, or if it’s a combination), have you looked at the world lately? You don’t have to go looking for missing faith as a reason for depression when the absolute shit storm brewing currently is there.
And the younger folks? The kids and very young adults I know, their anxiety is very much linked to the world trying to be shittier instead of improving. Maybe that won’t happen, but I don’t know anyone under 21 that isn’t dealing with some degree of anxiety post covid. Hell, I don’t know many adults that aren’t.