My parents were from St Louis, but I grew up in the 1970s-1980s out in the country 8 miles from a town of 1300 in southwestern Wisconsin. We had a zillion animals (sheep, ducks, geese, goats...) and a HUGE 1-acre organic garden. That, combined with my dad's hunting and fishing, and the 100 chickens we raised for eggs and meat every year, provided most of our food.
Spiritually (for lack of a better word) I loved it -- I am an introverted nature person, so it was very meaningful for me to be out in the country. Socially and culturally, on the other hand, it SUCKED. Especially after age 12 or so. Very conservative (as in hidebound, fearful and resentful of outsiders, which was anyone who didn't have 3 generations in the cemetery). Doing well in school made you a weirdo. Being interested in things like music, reading and art made you an even weirder weirdo.
Few people with degrees beyond high school. Antiquated ideas about gender. Racism of both the nasty and the clueless variety. Little interest or awareness (in fact, sometimes outright hostility) toward anything that wasn't local and rural, and then only if it fit certain pre-existing categories. Lots of fear and resentment toward anything "different." My friends' parents were afraid to let them go with me to movies in the college town 40 miles away because it was a "big city" of 200K people. (Yes, you had to drive 40 miles to see most movies.) I knew people who had literally never been out of the county. Not country, the county. Who had never been on an airplane. I mean, nice people, but. After a while, and after you weren't a little kid anymore, it could be hard to find something to talk about. Nutty evangelical churches. The local restaurants today have the same menu they did 35 years ago, and the songs on the jukebox are the same too.
No jobs except the local factory, the fast food places out on the highway, in tourism, or in the school district. I know people who commuted 40-60 miles to work each way, every day. For decades. (My dad was one of them. He worked FT on top of all the self-sufficiency projects, which my mom had to deal with on top of taking care of 2 kids. She canned like 300 pounds of tomatoes every year and was the one who initiated the divorce. I ate amazingly well as a kid, though...)
There was a small (much larger now) artsy-hippie-bohemian component to the area, which did help--especially the one restaurant-cafe where they all hung out and which was the only place within 30 miles where you could get vegetarian food or hear music that wasn't country or classic rock -- but basically every one of them came from outside. And after a while you could see that they were a pretty monocultural group too.
Kids started drinking until they puked in 8th grade and it seemed like every year a couple of teenagers were killed in alcohol-related car crashes. Nothing, nothing, nothing for teenagers to do but drive around getting wasted or going to parties 20 miles out in the country and getting wasted there. One high school with 300 kids -- and if you didn't like it, you were stuck. There was literally noplace else to go.
I'd say maybe 30% of my class went to college -- including technical school or community college -- and half of those dropped out.
And if you were LGBTQ, FORGET IT. At that time especially, there was no chance for a teenager to even come close to being out. Years later I discovered via Facebook that probably half the people I hung out with most in high school were gay, and every one of them had gotten the hell out the minute they could. Today it's probably marginally better, but I know at least one person with a trans kid who moved away a few years ago because it was clear that life as that kid was going to be intolerable in that town.
I still miss where I grew up a lot, and dream about having a little place in the country myself sometimes, but a few years ago I stayed in my old town for a couple of nights and left thinking, with utter conviction, that you could not pay me a million dollars to move back there again. (I spent 20 years in NYC and Boston, where I did always have a garden. In Boston especially.)
And again, this is actually a fairly cultured place for a small rural area. (Like, they have a BOOKSTORE now, and it's a good one.) This is a place I MISS -- the nature part, at least. I mean, I'd maybe do a vacation cabin or something, but I would NEVER make my kids be teenagers in a place like that. Never.
Younger kids can love it, especially if they are very good at entertaining themselves (which I was -- even today I can happily spend days on end alone doing projects and hanging out in the woods). My brother did not love it. At all. He would have much preferred to live in a neighborhood with a lot of kids to play with, and he was very lonesome a lot of the time. He has zero nostalgia for where we grew up.
I do wish my older kid could have lived in the country for a while, as he would have really liked it. I will not be at all surprised if he ends up doing some sort of rural thing for a while when he leaves home. The younger one, though, I think is probably more like my brother.
Oh, and as many people have mentioned, doing the self-sufficient thing is a HUGE VAST AND UNENDING amount of work. I never did that much as a kid, but it eventually broke up my parents' marriage, and I am sure they are not the only ones. (I am thinking in particular of an idealistic couple that moved out there to start an organic CSA farm. They had three kids, did the total back-to-the land thing, and had a gorgeous property. Within about 8 years they were broke and divorced and went out of business. So. The quality of your relationship is very important.)
There is also violence. You also have to be willing to do things like shoot or otherwise end the lives of injured livestock. Kill bunnies and chickens and deer and cut them into pieces (if you eat meat). Dogs and cats can get hit by cars, or shot by idiots. You will see roadkill constantly.
Because you have to drive.absolutely.everywhere. Not just for food or the post office. Kids taking music or swim lessons? On a sports team? Want to see a movie? Hang out with friends? Drive, drive, drive.
In other parts of the country, the rural culture is probably way better than where I grew up -- New England has a lot more interesting things going on (like in Western MA's Pioneer Valley or parts of VT, where you can live in the woods and then drive into town to catch the Amtrak to NYC or Boston), so if that's where you are looking then maybe it would not be so bad. The West Coast is probably not bad either. But just keep in mind that someday your kids are going to be 15 years old. What will life be like for them?