The "garden city" movement was a thing, but not quite what you're describing. "Towers in a park" was an organizational scheme for cities proposed by Modern architects, such as Le Cobusier in his Ville Radieuse proposal, and is maybe more like what you're thinking.
Brasilia is definitely the kind of alternate future garden city I'm thinking of. I mean, can you imagine walking between buildings at opposite ends of that area? In that heat?
Why not build taller buildings? Crammed together on a grid, provide underground walking areas?
Perhaps there is a different term for the type of city you are thinking of, generally cities such as Letchworth[1] are moreso what is known as a garden city.
Letchworth is a Garden City. Brasilia is a "towers in a park" type Modernist city. You're interested in "towers in a park."
Historically, cities like Brasilia were designed around the logic of the car. For example, most roadway intersections feature over and underpasses, cars are completely segregated from pedestrians. By most accounts, it doesn't work so well.
Why not build taller buildings? Crammed together on a grid, provide underground walking areas?
There's certainly no shortage of cars there https://www.google.com/maps/place/Bras%C3%ADlia+-+Federal+Di...