The 300C had a kingpin front suspension and live axle rear suspension not all that much different than what I had on my Plymouth. I have pushed cars like that until the wheels flexed under cornering loads to the point of jettisoning hubcaps. I vividly remember one popping off the right front on Sepulveda Pass one day on a hoon and watching that big stainless steel hub cap almost hit a Mercedes Benz that was nosing out of a side street looking for an opportunity to make a left turn. I dialed it back a notch after that day.
Here are the sorts of parts you need to make an old car from the 1950s and 1960s handle well.
http://www.hotchkis.net/dodge_b_e_body_geometry_corrected_tubular_upper_aarms.html
Even with the old torsion bar suspension the geometry was not modern. They still had positive camber gain, which prevents the tire from being perpendicular to the pavement when the car rolls in a corner, limiting how much traction and cornering force you can generate, and they had excessive caster gain. They were better in some ways than some GM products because GMs had soft bushings and needed a Panhard rod or Watts Link to control rear axle side to side movement on their coil spring rear suspensions (if you exited a driveway diagonally you could feel the rear of the car moving side to side from bushing flex), but a mid 1970's Chevy Nova will spank a same year Plymouth Valiant or Dodge Dart for handling because by then GM had a better front steering geometry (same front end Camaros and Firebirds were using on pretty much the same front subframe) and GM was by then using a single leaf rear leaf spring so there was no sliding friction between leaves as you had with Chrysler products of that era. It was still a live axle on leaf springs but it was the best developed leaf spring suspension on the market.
A big shortcoming of torsion bars as a spring is that you cannot build in a progressive spring rate as you can with a coil spring. You are stuck with a straight rate spring. It does, however, minimize unsprung weight and is easy to package. I think it was more marketing that good engineering however. Coils give the suspension tuner far more options.
Btw, if you build a car with enough body stiffness, it doesn't need to be sprung hard. This is why Mercedes Benzs and BMWs of that era could have a creamy smooth ride and still handle so well. A big S class rides as softly as a Buick, but Mercedes had vastly superior suspension geometry at both ends and their bodies were so rigid they could use soft springs and still have excellent control. With most American cars of the era, their bodies flexed so badly under cornering loads (push an early 1970's Corvette on some bumpy corners to see what I mean, every body panel is flapping around, the ladder frame is twisting like Gumby and it is real work to hit your cornering line precisely but any body on frame car has problems when you push them hard in corners) the suspension mounting points were moving relative to each other making steering precision impossible. On old Cameros and Firebirds the firewall was not stiff enough for the front subframe and if you pushed them hard enough in corners you would crack the windshield. US car bodies were uniformly weak. Our engineers didn't know how to build a torsionally stiff body. To compensate, high performance American cars tended towards very hard suspensions to limit suspension travel under cornering loads. In effect, body flex became part of the springing of the car. Most US cars tended to be floaty boats that never threatened to flex the body, their limp suspensions led to loss of traction before they generated loads sufficient to flex the body.
Chryslers of the sixties had less body flex than most Ford or GM products of that era and thus had a bit better controlled suspensions but they still lacked a modern front steering geometry and still had miserable leaf spring rear suspensions. Drive a BMW hard on a bumpy road and drive 70's Chrysler product on the same road and see what I mean. But the BMW will still pamper you with a soft ride.