On the weekend when there's no traffic, it's easy enough to drive to a park, sure. During the week, when I would want to relax outdoors after work, all the parks you mention are a 30+ minute drive in stressful rush hour traffic.
(it's also worth mentioning that for my first 1.5 years in Atlanta, I couldn't even afford a car, so my options were limited to Piedmont Park and the Georgia Tech campus)
In rush hour traffic from the Atlantic Station area, according to Google Maps:
Grant Park: 26min drive
Centennial Olympic Park: 15min drive (I did go there all the time but it's not really a park? plus tons of car noise nearby)
Freedom Park: 34min drive
Candler Park: 28min drive
Chastain Park: 28min drive
I'd occasionally go to the park along Collier Road or to Memorial Park (both 15-20min drive in traffic), but both are surrounded by deadlocked rush hour traffic for most of the afternoon.
I think the lesson is maybe that I should've chosen to live in the Little 5 Points area or somewhere east of Piedmont, but that would mean sacrificing my ~5min bicycle commute to the Georgia Tech campus where I was going to school at the time.
In the end Atlanta's car culture really grated on me, so I left.
That said, I think Atlanta is on a positive trajectory. I'm excited to see how the Microsoft campus impacts the western part of the city. I imagine in 15-20 years it could be a really appealing city.