Whether or not a certain religion is "proven false" is generally not a productive question. But many religious people would proudly state that they would continue to hold whatever sacred belief they have even if it were proven wrong. So I think the popularity of religion does show that people want to believe false things, regardless of whether the religion is true or false or (most commonly) unfalsifiable.
Well, maybe not, but most of the big ones are at least mutually exclusive. So to the OP's point, at various periods throughout history at least ~80% of the population were "believing false things", even if we can't agree on which 80% those were.