It's too bad, I think idea of organizing a social network based on proximity and centered around community information is a viable idea, It's just that NextDoor is doing that with our worst instincts.
NextDoor and Craigslist and Reddit's /r/{city} communities just prove that it may be viable but it's pretty undesirable. I think it's best to not give the most neurotic, ill people of your community the loudest voice, but these social networks also create this neuroticism and illness.
You also create a scenario (NextDoor especially) where all the sane people are driven out by the crazies. Back when NextDoor was new, after a year it would come up in conversation and sure enough, anyone normal would admit they tried it and had to delete it.
Social media is messing us up. I don't think we're missing some new take on it that's going to make it all better. I think the vestigially tribal parts of our brain make it a non-starter. We need to get back to the face-to-face -- it seems to be the only way we keep in mind that there's a human at the other end of the line, not some nebulous automaton that we craft into everything we hate in the world.
I agree that the behavior being capitalized on here is pathological but using the terms "neuroticism", "illness", and "crazies" here unfairly and wrongly stigmatizes people with mental illness when in practice people with mental illness are more likely to be harmed by these suspicious posts and behavior nextdoor had been encouraging