I wouldn't. My parents did a similar move when I was 10. The next 7 years were incredibly isolating and boring. The other kids my age didn't really share any of my interests (most of them were being groomed to take over their parents farm/work on their friend's farms-I was into art and books and theatre), and unlike where we used to live, there weren't any places to make friends other than school. The kids in scouts and all that were the same kids you saw at school. I did have people to hang out with, but no real friends. They were nice people, but if I'd have thought no one would make a big fuss I would have rather have just had books for friends. BTW, all that crap about kids in the city being wilder...by the time I was 16 half of my peers in the countryside were either drug addicted alcoholics, pregnant, had criminal records or all three. Oh and an obscene amount died or were terribly injured in car accidents, most of which were caused by idiot kids playing chicken in stolen cars and stuff like that. It was easy to understand though. Live in a place where teenagers have nothing to do, they're going to make their own fun.
By living where we did I lost the opportunity to do a lot of things. Where we used to live there were lot's of free and cheap activities, there were museums and amazing libraries that ran all sorts of classes and events. In my new town there was really nothing. Loitering outside closed shops for 5 hours was considered a fun activity. When I was a bit older, I couldn't get any sort of job. There was no work in my town for teenagers unless their parents owned a shop, and we were too far away from bigger towns. I had tons of interviews and so many places told me I was perfect but I lived too far away. They wanted someone who could get there by themselves eg. not relying on mum and dad or a bus that ran every 2 hours, and they were right to. If I had gotten a job public transport wouldn't have cut it, I would have needed my parents to drive me back and forth most of the time, and I know they would have tired of it almost immediately. Meanwhile the few friends I kept in contact with in my old town all had jobs, and they also got to do some work experience and volunteering that greatly helped them later on. I had trouble getting work later because I had nothing on my resume when most people my age had at least a few work experience spots. Oh and the school I went to was terrible, there was definitely an undercurrent of 'everyone's going to be in this dead-end town forever, just like their parents and their parents parents, no point in bothering really'. The closest schools were the same, going to a decent one would have meant a 3 hour round trip, so never a viable option.
Probably the biggest thing was the lack of independence. I was very reliant on my parents to get anywhere, and because of the work situation I was also completely financially independent. I honestly had a lot more freedom aged 10 in a big town than aged 16 in a small village. In the big town I could walk to school, to nearby friends and shops, to the library etc. because there were so many people around, in the small village my parents wouldn't let me go anywhere by myself til I was pretty much an adult (and even then they didn't like it), because if anything happened there'd be no one around to help or even witness it. And like anywhere there were some real creeps, but due to the small population they knew my name, could easily guess where I'd be etc. I felt/still feel a lot safer in big towns and cities.
Oh and other posters are right, unless it's a big pre-planned thing like a concert, most teens just make plans on the fly which makes it really difficult if you're reliant on someone else to ferry you around.
Sorry to be so resoundingly negative, but I really hated living in the sticks. I moved the second I was able to, and life immediately got a million times better. I honestly feel living where I did held me back. I wouldn't mind living in the countryside as an adult, because now I've had fun, I've seen things, I've had opportunities, I've travelled...now I'd be ok with a bit of isolation and a nice, simple but rather dull life. But I'll wait til the DC's have left.