I live in a block of flats outside the UK. We have good soundproofing, elevators (more than one!), a big communal indoor mingling area on the ground floor, community rooms you can hire, a big bollarded outdoor space for kids to run round on, greenery planted round the building etc., and spacious balconies you can hang your washing on.
Apartment living done well is great. I love the sociability and central location. Yes, you have to pay service charges, but this has to be balanced against very cheap heating costs and not having to run a car, which saves a fortune. Stairfree living makes cleaning, laundry and childcare easy, and means you have no worry about older relatives or the long term picture. My 12yo can be incredibly independent and go most places by herself; I don't have to spend time carting her about.
My parents live in a suburban house in an area where everyone drives. It's nice, but you just exchange one type of hassle for another. You don't have to worry about little kids playing up on public transport, but you do end up worrying about car parking, getting stuck in traffic, and blinking car seats. The garden is pretty, but the time of year when it's usable is limited and kids quickly grow out of wanting to play there. We mostly used parks even though the garden was right there.
It's possible to have a house in a central location by doing the "tall skinny townhouse" thing. You can have rooftop garden where I live, and these are very nice and quite tempting! On the other hand, these houses lose so much space to stairs and landings, and you are up and down the million stairs all day with hoovers and kids' stuff and bin bags and shopping and what not, big hassle with prams and naps and stairgates (and older relatives). Nice but not my preference. It's good to have lots of choice so we can all live in our preferred type of home!
The UK would do better with apartment living if:
a) it reformed the leasehold system
b) apartments had proper sound proofing and balconies, enough bedrooms, etc.. child friendly spaces. There should be laws against rules stopping people putting washing out, seriously!
I think a big problem in the UK is that the last big spate of apartment building happened in the 1960s or so. The apartments were poorly made and not very nice at all, and were made to house the least advantaged people in society. This created a really bad image problem that has lingered to this day. What's more, this process coincided with a big crime wave and I think an association of "high rise living --> crime" formed in people's minds and has been hard to eradicate. It's complete nonsense; international comparisons show that crime went up sharply in the 60s everywhere, regardless of whether countries were building apartments en masse or not!