Choke input filters were common on large old 50Hz power supplies .The size of the choke combined with a lack of understanding about distortion factor and cheaper caps favoured the cap input filter which is popular today.Swinging chokes were manufactured for these old power supplies .The swinging choke used at least 1 step in the laminations to give at least 2 different air gaps . Partial saturation gave big inductance at low current and small inductance at high current.This is precisely whats wanted .If the load was fixed a normal choke would perform fine.The choke filter is back with SMPS because the choke is not huge anymore .Why has nobody done a swinging choke for say a full bridge SMPS ? Would say angle grinding the ferrite core on a SMPS choke have a similiar effect? Could the losses be acceptably low because most of the ferrite is not saturated? Could the new distributed gap ferrite powder coils from WURTH that show a gradual inductance fall with current be relevent?
Based on this description I think swinging choke was a somewhat primitive way of doing voltage regulation, or rather load regulation straight from a bridge (or center-tapped full wave) rectifier + filter.
If the rise produced by the swinging choke just offsets the losses produced by increased current through the rectifier, the power transformer, and possibly a further smoothing choke, the output voltage of this kind of filter will be almost perfectly constant as the load current is changed.
In an SMPS you do that voltage/load regulation by different (electronic feedback) means, typically by controlling the duty cycle, so I don't know what sense it would make to try and use that swinging choke method.
In general with SMPS designs one avoids saturating the output inductor (choke) because that will give you at the very least worse ripple, efficiency loss in the inductor, ultimately as heat and even possible destruction of the switching element. Finally some SMPS control schemes assume the current raises linearly thorough the inductor.
Having said all that, there is some research on driving SMPS output inductor into saturation. I wasn't aware of it until a few moments ago... The main motivation for this research was to use a smaller inductor thus minimize board space, rather than gain some sort voltage regulation from it (in that respect you get the opposite). Basically their argument is that footprint reduction gained by driving the inductor into saturating is worthwhile in the cases where:
- the peak-to-average-power ratio is high so most of the time the converter's inductor won't be saturating, and
- the increased ripple at high loads is tolerable because (for instance) one also has LDOs doing additional filtering thereafter for the most sensitive circuitry.
They also say that the latter issue can be addressed by "hysteretic converters". I don't know much about those.
Regarding your inductor examples from the comments below: an inductor doesn't become a dead short when it saturates, but rather becomes an air-core inductor... which does have lower inductance but it's not necessarily negligible. For the inductors in the aforementioned paper, the drop was to about 1/3 inductance at saturation. This of course can cause havoc if you haven't planned for it when choosing the switching element, but if you did, then it will of course survive.
And regarding inductor design for "partial saturation": I'm a neophyte at magnetics, so I can't say how to design one that has a gradual slope increase rather than an inflection point, but certainly it is possible considering the examples at http://elm-chan.org/works/lchk/report.html If you intend[ed] to ask how to build/choose such inductors, you should probably ask that as a separate question...