Sure, but there has also basically been no secular societies to speak of at all until relatively recently... Like I'd love to see you name as many as you know just to see how many you get beyond "Soviet Union", which had a bunch of issues that would lead to it's collapse beyond the lack of religion.
It seems unfair to say "oh there hasn't ever been long standing secular societies, therefore something about secularism causes social breakdown" when barely any secular societies have ever even existed
I’d argue that Greeks were about as secular as modern Canada or America are. There was the concept of religion but it wasn’t relevant. There was also a push towards leaving religion behind as evidenced by philosophers.