Back yard? That does not exist in the US. You get a tiny garden which is not enough.
In Europe we have the various sport fields you can reach on foot or via light rail, not even going into a car. Therefore your kids do not have to drive at age 12.
You can reach work via train, I know people who ride in excess of 200 km daily.
Heck, schools and universities are reachable via such transit.
We have big parks in the cities.
I am not talking cities the density of Hong Kong either. NY is not quite walkable either, it lacks walkability due to grid street design with no accommodations for crossing them easily and safely.
Parks in big cities are completely different from large yards. Parks are nice, but large yards mean you can have gardens, grow food, or have lots of friends and family visit.
You are only correct if "semi-rural" to you means "suburban".
Granted that new neighborhoods seem to be built with less care for yards, but growing up in suburban Texas in a subdivision from the '60s, we all had decent yards to play in, with room for trees, gardens, and sometimes even large swimming pools.
I live in an urban area now, and love it. But people need to open their minds and stop crapping on other peoples' lifestyles.
People saying "I just can't /imagine/ living 30 minutes from the citycenter" are as close minded as those who can't /imagine/ living in a walkable area with shops and food nearby.
You see kids playing around in city parks pretty safely, and people who want the suburbs live in villages on commuter rail about 30+ minutes away. They actually have apartments in the city core that are 2000sqft and can have 3 large bedrooms with a big living room and hallway with plenty of sunlight. The interior of the apartment buildings create a court yard with a little playground and you often see kids there, playing together. They are very pleasant, and all of these people don't need to have a car.
Interestingly, many studies suggest that urban children are significantly more free range than suburban these days. (does not isolate for race/social class)
My parents live in an inner streetcar suburb of Milwaukee, have plenty of living and gardening space, and are a shorter walk to a movie theater than I am in Brooklyn.
I favor medium-density inner Brooklyn myself, but I grew up in the suburbs, with a few dozen acres of woods behind the houses, and I'm glad I did. Suburbs are demonstrably awesome too.