The fact of the matter is all springs wear out or loose their spring. And t the Airstream design isn't old! It is far newer than leaf springs.
Torsion axle design with rubber rods has several advantages as noted above.
Torsion axles incorporates the axle and springs assemblies in a smaller space. That space is used to expand the coach and storage in the coach. Another reason why shocks went from vertical mounting to horizontal mounting in 1967
Torsion axles offer a soother ride. Yes each wheel is independent from side to side and from front to rear in multi-axle set ups.
Torsion axles can offer a lower ride height and/or center of gravity.
As noted above torsion axles are very simple in design with much fewer moving parts. Less parts to go bad. While it isn't a totally radical design as Chrysler Corporation used torsion springs in the late 1950s across the entire car line up. Packard used torsion springs before that.
Down side to the Airstream design -
They are much more expensive than a leaf or coil spring designs
The axle assembly in not serviceable. If the springs need to be replaced it is done by replacing the axle too.
For trailer that sit unused for long periods of time the torsion rubber rods loose their flexing properties. The rubber tends to harden.
The use of this axle type is on a much smaller production level than most other springs. So many of the companies listed above failed due to the lack of sales. Especially in the economic down turn that occurred in the last almost 10 years.
Hope this helps.