It's really the same problem they've had going back to the Josh Smith-Joe Johnson days in that they don't have a consistent, reliable bench on both ends. Their starting five can be great (this one more so than that one), Horford is a really really great player, they've surrounded him with even better pieces now, but the bench is still pretty garbage. Schroder and Mike Scott and some others seemed to be changing that this year which is how they bumped up to 55-60 wins instead of the expected 50-55 wins but it's same problem dating back to Jamal Crawford's sixth man year. They don't have the depth which you need when you don't have a LeBron or either next-tier talent. In the playoffs, those guys don't sit, so you have to outplay the other four positions throughout the entire game. It's how the Pistons/recent Spurs have done it without an elite-level player. You can't drop off too far when you go to the bench. The Hawks do pretty hard.
They didn't have a great window because of Korver's age and how Carroll's going to get big bucks. They could reasonably get another shot at it or two. But Thabo and Kent Bazemore can't be their big signings. Especially if they're paying Milsap and Carroll $20+ million combined.