Well, yes, and no. With an all-out race car that lives on a relatively smooth track with little to no bumps, a car with stiff springs and proper suspension geometry wouldn't need sway bars. Heck, shifter karts have NO suspension, at least the ones I've seen, and they handle like they're on rails. But take that same car and run it down any normal street, especially a concrete paved one with seams and potholes, and it would beat you up so bad that it would turn your insides to pudding!
Suspension designs for the street have to keep comprimise in mind. Enough suspension travel to survive bad bumps and potholes, and springs not too soft, but also not so stiff that you end every drive in pain. That's where sway bars come in, they reduce side to side roll without raising the spring rates very much.
Roll bars ARE a band aid, but they're a very necessary band aid for a proper handling street car, there aren't many other simple or practical ways around them, especially in the same price bracket.
Oh, and back to the original intent of this thread: Don't forget GOOD shocks, they can change the handling of your car as much as sway bars! And don't be afraid to try the junkyard sway bars, the suspensions on our favorite muscle cars are so far from being corner burners that it's hard to not make an improvement!