As one who willingly moved from various built up areas (most recently the Seattle east side) to rural farm country to be near family and a place we actually enjoy living (instead of hating)...
A big part of it is simply that my wife & I weren't happy in dense areas. We've tried it, we tried the stuff people insisted we should do, and... after 4 years in the Seattle metro area, we hated it more than when we moved there. The money was nice, but we were both stressed out, and simply didn't enjoy the place. The stuff we care about (generally being left alone, quiet camping in the middle of nowhere, family, etc) it didn't offer, and the stuff it did (Chinese delivery at 3AM seemed very important to people for some reason, a variety of restaurants, etc) we simply didn't care about.
Most activities seemed to be "Sitting in traffic to stand in line to spend money." Those who liked the area informed us that we were doing it wrong, and we should be taking public transit to stand in line to spend money - didn't really alter our core problem with the concept.
A favorite sport of mine, when people talked about all the art galleries and museums and (etc) they loved living by, was to ask them when they'd last actually gone to those places. Almost universally, the answer was some awkward noises that eventually translated to "Well, never, but... I do like having the option!" I live near plenty of little museums and art exhibits, but they tend to be small town museums (great fun for the free summer festivals most towns have), and more private art collections/murals/etc. Out here, a good amount of that is actually from my wife's grandmother - she was quite active for many years, and she's been part of countless murals out here. Unlike in dense areas, murals can survive quite nicely for decades out in farm country.
I'm curious what about rural life you want your kids to experience. Maybe you have an idealized version of rural living envisioned in your head, but we were developing concerns losing out on educational experiences.
What educational experiences can't you create? Our cost of living is low enough that we can (and likely will) home school, travel during the school year to museums, etc.
Rural living is a whole hell of a lot of work, which is also quite nice to teach kids. Seattle was, for me, a horrifying place -
nobody could do anything. I watched two grown men struggle (and fail) with the concept of using
two wrenches to loosen a pipe connection - though, admittedly, they were only trying to do that because they listened to the sales guy instead of reading the manual that came with the tankless hot water heater. Nobody had thought through using a propane tankless hot water heater indoors either, and the particular facility had to inform them that, no, they were
not going to be lighting that thing in their exhibition hall, there's the door, here are some hoses, thank you very much. It was a long night babysitting that thing for me... since I forgot that whoever solves the problem now owns the problem out there. But it was alternately comedic and sad, seeing how little grown adults were either willing or able to do themselves when it came to the physical world.
Out here, repairing and fixing your own stuff is just a normal part of life. I specialize in a bit more esoteric repairs than many people (small electronics, battery packs, etc), but I can wrench on a vehicle quite competently as well.
As resourceful mustachians, there's never "nothing to do" no matter where you live. However, in a rural area there's a feeling of lack of breadth of experiences. You can't learn city or street smarts in rural america. But you can experience that in a city and then I take my kids camping regularly and teach them bushcraft on my own when the opportunity arises. We make the kids do as much chores living in a city vs sticks. The only thing they will not learn is lawncare, which I think is a wasted skill anyways.
Alternately, you can't learn agriculture, animal husbandry, and an awful lot of other things in the city. If you're out towards the edges, there might be a 4H club (unlikely to find FFA near in), but they're pretty hard to find.
It's easy to visit cities for a week or so and see what they have to offer. It's pretty hard to get to learn a rural lifestyle without actually living out there for a while.
Though, in cities/suburbs, an awful lot more people care about the state of your lawn than in a rural area. HOAs tend to be really cranky about letting your lawn be anything but chemically synthetic green.
We were also developing a concern for lack of exposure to diversity. There's a serious lack of diversity in most rural places, not just race, but also lack of diversity in ethnicity, culture, religion, political views, even as trivial as food choices, clothes people wear, or cars. I could say these things because I actually lived in rural missouri. My wife agrees and she grew up in rural illinois in a town of less than 200 people. Of course this was just my own personal experience, and shouldnt apply to everyone.
And... how often do you actually bother immersing yourself in that diversity? We certainly lack a diversity of cars that cost more than our house, but I don't really feel my kids are missing out on that front.
On the other hand, my tractor does cost more than an awful lot of my cars - and it's not that expensive a tractor.