Staying below 2000 people per square km will make it difficult to provide good public transport or other amenities, including shops. Anyone able to afford a car will want at least one per household, further reducing the population density and making it harder to get around on foot/bike/bus. Ultimately the only people who would choose this form of low-density living over conventional suburban homes would be those unable to afford their own house. Pleasant landscaping is expensive to maintain and almost guaranteed not to happen for a handful of poor people so you'd either end up with impenetrable forest or bare grass and concrete between buildings.
There are a few cases where something like this works quite well, but generally only the highest density versions when located in or near a large, prosperous city that already has excellent amenities. Otherwise it tends to be a disaster.
Optimizing for one thing alone rarely works in urban planing, even if the idea of ample green space for everyone seems uncontroversial.
About Le Corbusier. His core idea is interesting but from what I've seen the "towers in a park" implementations are basically "massive ugly badly designed towers surrounded by a malnourished slivers of grass". Also, for those: 1. the population density is invariably way too high, 2. the towers are always massive, 3. the green space sizes are absolutely too small, 4. the "green spaces" are boring and/or half dead, many times only grass (why not have gardens that actually produce food for people who live there, or forests)?
For example, Stuyvesant Town is one "tower in the park". It is IMO too crowded with too high towers. Reduce number of towers to 4 or 5, make towers lower, and it'd be more like it.
To give an exaggerated example, if one were to put a 6 floor tower right in the middle of Central Park, that's what I'm kind of after...
Why does having a car reduce the population density or impact foot/bike/bus at all?
As for the density cutoff of 2000 people / square km. Here we'd have a building of 100 people, 40 apartments (assume family of 2.5 people), 5 apartments/floor, 8 floors. Tower footprint won't make a huge difference, let's say it's > 500 m2, and this would be 1..2% per tower total area. In 1 square km (100 hectares) we'd have 20 such towers á 100 persons, thus 2000 people per square km. The towers would be quite low, and this would still be "dense enough" per that cutoff.
(This is napkin math so the real number is slightly lower or higher depending on various parameters)
Anyway, this an idea I'd like to see happen. I'm not an architect/planner (perhaps for a reason, say the shouts from the audience).
PS. https://www.sweco.se/projekt/satra/ this project (in Sweden) aims to build greenspaces where inhabitants can produce food. That's the theory at least, it will be interesting to see how it turns out. I do think this is again way too dense, but greenspaces to produce food is a great idea.
One tenth of that might be workable. One hundreth is probably fine. Gives the apartment building a house-sized lot for garden. And gives neighborhood a block sized park. And gives the city a large, nature park.
As others have said this density is just way too low. It's an improvement on the status quo that exists in many areas (low density sprawl with individual private green spaces, but essentially no public green space) but this density is just not good enough to create walkable communities.
The only city I've visited that seems to get this right is Chicago, which has massive tracts of public land that are accessible to everybody by walking, cycling, or public transit.
Not everybody will be able to live right next to a park, but nobody will live very far from one, either.
I don't know what people think are a biking/walking distance, but a distance of 1 km is walkable in ca. 15 minutes. Bicyclable in some minutes during summer.
More density than suburbs is really OK for a city core, but too much density is bad... Everyone should reject that. All the building projects I see are just concrete upon concrete, too dense, no green, just awful.
I would love to see more integrated greenspace instead of "hey, there's already a smallish park 2 km from you, go there to weep you hippie". Hence the original idea.
I guess some who are actual planners/architects are shooting it down, which is great, I can then imagine something better :)
The average backyard size in the US is 2,164 m2, which would support a family of 4 in your scenario but obviously suburbs full of backyards don’t actually feel very nice and green. Central Park is so amazing because it is adjacent to high density NYC. You have the amenities of a city and a large greenspace. NYC is hyper dense, but that is closer to optimal than rural Georgia.
Your Central Park example also points out another issue, which is money to maintain these greenspaces. At a fundamental level, it is a case of not having enough people to pay taxes (or whatever) for something even 10% as nice as Central Park. So you are back to what PartyOperator said, either bare grass, or wild forest. Another aspect is that people move to cities for a reason. Living in higher density allows for much greater and easier economic activity. Work From Home is nice for the few types of jobs that can do them, but most people need to go to work and doing that is only feasible with density.
Looking at your Swedish community example, that is only possible with density. You can even see from the overhead map that it is mostly smaller, hyper local parks and other mixed use areas, with a larger more unmanaged greenspace around the outside.
You can’t have your cake and eat it too. You can’t have the density of a deeply rural community, and also have huge, managed greenspaces and local shops. You should look into Strong Towns [1], that has a lot of good actual city planning information and what makes a happy, vibrant community.
The argument of closeness of amenities prioritizes a consumption-based lifestyle over building good nests for humans (and little humans) to actually live in. Let's take your example, where you said people don't like to walk 1 km to a small convenience store -- is the assumption somehow that walking 1 km to reach the tiniest park is something people would like?
As for jobs, I'd say very, very few people live in a city next to their jobs. They have to commute in one way or another. This seems to fall mostly between 10 minutes to 60 minutes when discussing with people. Time-wise I'd say this range is aligned with a smaller town/city (either a job in the town/city, or in another town/city).
And speaking of enjoyment, to be honest I'm not convinced many people in big cities really enjoy it. I'd wager to say that most people generally would enjoy a less noisy and overall cleaner environment where nature is nearer than concrete. Not everyone, but most.
My childhood town (in Northern Europe) is 31 people/km2. It's overall about 80 k people (lots of empty space). Density-wise it's probably something like your rural Georgia but everything one needs is there, plenty of shops and businesses of all kinds and even some variety in restaurants (believe it or not). Quite many people could actually do with a bicycle or a bus, but in practise people have a car because of winters and four seasons and because buses don't run all the time and reach everywhere. So then, for example, most people do groceries once a week and drive that 3-10 km to the grocery store or mall concentrations. But based on my experience, they would likely do exactly the same thing in a bigger city too, since the inner-city core grocery stores are more expensive with less variety.
Also, there's a spectrum between bare grass or wild forest... For example, where I live now one might have a "wild" forest designated as a "park", and someone from the municipality just cuts away the hanging branches, windsnaps and such and ensures the paths don't grow shut. It's very low effort and cost. Once in like 5-15 years they might cut some more growth of trees so there's more sunlight everywhere. This type of "park" does not have manicured golf course like grass areas and fountains and so the per year per area cost are much smaller.
So it's not about the cake and eating it, it's about having a different kind of cake.
Anyway, thanks a lot for the link!
Edit: PS. I followed your link now; the concept of Neighbourhood Park is a neat one. That is kind of what I mean, more of that, not necessarily with golf course lawn. Also, the "John F. Collins Park in Philadelphia" looks great!
As a concrete example: to build a building for 100 people, one must have 100*500 = 5 hectares of space around the building, reserved for a green space only, not parking lots or such.
Buildings would be more spaced apart and would not trap heat so much like traditional dense designs, so urban centers would be cooler. I dare to claim that people would be less crazy and generally happier and healthier when living like this. Over time, building less densely would see all kinds of positive effects compounding.
The green space could be used for many good things, e.g. growing hyperlocal food like vegetables, potatoes or whatever grows well in the climate, for having tree-shaded places during warm days, for just having a piece of nature to go to quickly and easily. Smaller batches of forest shading a path could connect multiple buildings built with the same ideas, and so on. It would be possible to use bicycles or walk along these paths.
In a nutshell, if one has to build high, then make all multi-storey buildings like a stacked nano-village surrounded by a larger green area/forest. Based on my subjective understanding very few people actually like the ground floor so that's a good place to put local small businesses like barber, shop, bakery, café, and so on.