I think you're just romanticizing the past. When I think back about the time I think your thinking about I see:
Dwyane Wade missing the playoffs in '09. Only played 51 games, but his team was 10-41 when he did play.
Kobe missed the playoffs in '05, and while he got in as a 7th seed the 2 years after that, those were both on teams that wouldn't qualify most other years in the West.
Garnett missing the playoffs in '05, '06, '07.
Pierce missing the playoffs in '06 and '07, and got in with a 36 win team in '04. In '07 when he did play, his team was 20-27.
Iverson missing the playoffs in '04 and '06. (only played 48 games in '04, but the team was 19-29 when he did play).
Vince Carter missing the playoffs in '03 and '04.
Surely those guys were considered superstars at the time. I don't think it's any different now with Cousins, George, and Davis than it was for guys like Wade, Kobe, Garnett, Pierce, Iverson, and Carter 10-15 years ago. With those "superstars" on your team and nothing else, you could be in position to snag a #7 or #8 seed. Still you need other chips to fall just right to make it happen, some years it happens, some years it doesn't.