You’re basically right, but note even in the formerly AES countries, despite plunging into deep crisis, the number of atheists remain at much higher levels than it was before socialism - even in country like Poland. It’s most visible in Czechia iirc. So it does work. Few more generations (it was like not even 2 basically) and much more would disappear, though probably not entirely (see Japanese christianity emerging after Meiji restoration, though it emerged 95% reduced and heavily influenced with buddhism).

I think there isn’t much problem with disorganised and decentralised religions, at least as the party remains strictly atheist, but something like the catholic church is immense danger, the worse that every move against them, even for completely nonrelated reasons (again look at Poland where some priests were arrested for spying and other antisocialist activities) will be always portrayed as attack on religion, so the socialist country would necessarily have aim to remove their political power, most likely by expropriation of their property - something that for example again Poland failed to do (PRL even gave them some of postgerman land!) which caused unending trouble.

There are many reasons people claim religions including national heritages, family history, spiritual connections to some practice, or genuine superstition. Education can address the latter but struggles with the former.

All those aren’t as immutable as you probably see it, there are historical examples of all this changing more or less rapidly. I think it’s again that socialism simply did not had enough time and had too much outside opposition to properly adress that.

Lenin once wrote interesting article “On the significance of militant materialism”