Didn't those ones still have leaf springs?
They have 'em for a reason – because, on the packaging and weight front, they offer considerable advantages compared to a conventional set-up. Also, GM's perfected them over decades of use. They're not what you'd see slung under the back of an old Transit, either; there's only one spring at each end, mounted transversely, and they're typically composite. Have an integral anti-roll effect, too, further cutting weight and complexity from the car.
C6 is a stout bit of kit, even in standard form. A standard car with the Z51 Performance Package (chassis and brake tweaks) went around the Nürburgring in 7:59, which is quicker than a V8 Vantage, E92 M3, Honda NSX, Alfa Romeo 4C, Z4 M Coupe, etc, etc.
Not that Nürburgring times tell the whole story, mind, but should give it a little perspective.
Hell, even the C5 was extremely keen – have a look at the C5 Z06, for example. C4s are harder to handle but, even so, they rule countless autocross tracks in the US for a reason. Compact, comparatively light, stiff and endlessly tuneable... and as tough as a brick!