The motives were indeed good, but you seem to be missing a few things in places.
Bear in mind I'm in the UK, where Europe's post-war rebuilding was also large part of the motive. The American experience was necessarily a little different - no bomb damage, and a large profit from WW2, thank-you-very-much.
The huge areas of bomb damage, and decades of soot and other pollutants meant many of those fine classic buildings were looking old, tired and in need of sand-blasting, or at least a good wash. The 50s brought coal restrictions and clean air legislation, so pollution and smog had passed. Cars weren't yet common. Looking to the future concrete was "clean", and very much of the Jetson's future, and you got so much more of it for every pound spent. Steam trains, and Victorian gothic fussiness were of the mucky past. Yet unlike marble, granite and even sandstone and brick it so often weathers and ages horribly.
There was, as you note far more space - and in architect or promotional artistry before they were built this usually had trees, planting, and very often a view through trees. The other style was of people and cars as cells in the futuristic city organism - that Jetson future once again. The 95% reality had a few feature trees set in concrete or flagstones, some feature planters for flowers - horse trough or hot tub sized that in the sea of concrete looked comical afterthought. By the 70s the trees most especially were dying, horribly sad or missing. Turns out mature trees need more than 2 sq m of water capture. I remember very little grass in the brutalist bits of the city I grew up in or those I visited in the 70s and 80s. The sweeping walkways in the sky meant walking a mile to cross a road, or endless steps - horrible if mother with pram, and lastly plenty of dark gloomy spots to get mugged or lost in.
The pre-war modernist, or the garden city movements, and even pre-war social housing had, in the UK, far more of the natural world, grass, large grass verges with mature trees and play spaces or parks. They hadn't yet discovered separating shopping centre from housing, so they were still working communities.
So yeah, it's easy to see why they tried and the motives that brought them, but it's as easy to see why it so often turned out dystopian nightmare to be demolished as soon as affordable. We'll be stuck with those car-first choices for a century though. Today's alternative of finding lowest possible bid unless it's a feature tower block isn't that much better.