They stopped using them when front wheel drive and macpherson struts became the norm.
Chrysler used the torsion bar suspension because they provided better cornering then coils.
The XK 120-150 series Jaguars had torsion bars as well. They are a space saving feature when there is little room under the hood, as in the case of the Jags.
On the last generation of “real” Packards, prior to their brief existence as Studebaker clones, torsion bar suspension was used on all 4 wheels, in conjunction with air bladders. Those cars had an incredibly smooth ride and–for their size and weight–they also handled well.
Too bad that the system was very trouble-prone. As was said, problems with torsion bar suspensions stemmed from the execution of them, not from the basic concept.
I had forgotten all about the last real Packards having torsion bar suspension. I think that this would have been the 1955 Packard. I think that 1955 was the first year Packard went to a V-8 engine from the straight 8. These Packards should have been great cars, but as you said, while the concept was good, the execution was not.
My '89 Toyota pickup had torsion bars. Suspension firmness wasn’t a problem in the compact pickups and I’ll bet the torsion bars were cheaper to make and install.
Had an Toy 89 2wd Xtra cab v6 with that suspension too. Loved it. Great trip car in moving kids back and forth to college on those 600 mile trips and nearly full loads. Rode great. My favorite truck.