Having moved from an inexpensive neighborhood to a more expensive one, I think there is definitely value to neighborhood.
I would bet by crime statistics my old neighborhood was only a little worse than my new one will prove to be over time (although with only a 3 year history, there have been no reported crimes), the old one had a slightly higher crime rate because I was so close to a HUD development, and IT had lots of petty crime within it. But I never felt unsafe. I was near a police station though- about 2 miles.
However, the level of community in my new neighborhood is practically priceless. But if I could find a less expensive neighborhood like that, there is no actual value in the bigger house for me.
But know the name of everyone who lives on my street, seeing all the kids play together, having fire pits with the neighbors- these things are worth paying for, IMO.
NONE of this happened in my old neighborhood. I would wave when walking the street and people would glare at me, I would bake cookies for people who just moved in and never see them again.
It may not be caused by house price; but this was my experience, and the experience of many people who "moved up" to our new neighborhood.
So if the house is not a stretch to afford it, I totally understand the reasoning.