I've seen it discussed a few times in the pragmatic dharma community that there seems to be a significant increase in the amount of people attaining stream entry in the past decade or so. Assuming this is the case, wouldn't it be highly likely that a much higher number of people than that would be stuck in the dark night?

What sort of institution could be created that would allow people to discover that they're in the dark night, and effectively lead them to mitigate harm and progress out of it?

Possibly but more people getting stream entry could be due to more people passing out of the dark night. In other words, getting the backlog of people who are already stuck in the dark night out of it. So not necessarily the case that more people are going into the dark night. But who knows?