Talk to some really old people, who recall the 1950's. At least in America, there were a huge number of non-church social groups. And families tended to be both far larger, and considerably better connected.

If some churchgoer was saying, today, that the churches have some sort of monopoly on providing such spaces...my interpretation would tend toward "we have a monopoly, while we last, because every other provider is already gone".

(Yes, if you go further back, especially in Europe, the church had somewhat more of a monopoly. Partly that was because governments were rather authoritarian, and didn't want organizations to exist, beyond their tightly-controlled churches.)