My driving improved no end when I got into driving older cars.
Old drum brakes, no abs/traction control/limited slip diffs, no power steering etc, suddenly gave me a huge appreciation for good anticipation, driving at a speed appropriate for the conditions, and correct application of braking distances.
An issue I've noticed recently is that modern automotive technology is now at such a state where one can drive really pretty badly and 90% of the time the technology will get you out of trouble. For example, entering a corner too quickly and slamming on the brakes halfway round in most modern cars no longer spits you into a tree on the far side of the road in the same way that a car of 30 years ago would have done. this means that driving becomes a mental background activity for many drivers, so bad driving becomes self fulfilling.
Within that 10% area of driving badly and it really going wrong, it is then beyond even that scope of modern driving aids to recover. You then are seriously in the shit, as invariably it is a driver who has never experienced anything like this before in a car that is out of control to such an extent that even the various technologies cannot cope. A lot of the technologies also reduce the feedback to the driver. In an old car it is invariably easier to sense when things are getting a bit hairy and ease off, whereas in my experience of modern vehicles it seems a lot more binary (everything is fine up to the point where it all goes wrong).
I don't think it is feasible for all drivers to learn in old vehicles (nor is it a particularly good idea), but I think a power/size/weight/speed restriction for new drivers might not be such a bad idea. Such a vehicle would inevitably be small, slow and missing many of the "sports" features which facilitate poor/aggressive driving, thus learning would be improved.
I also think that driving lessons should contain a mandatory skid pan session simulating icy/very wet conditions to ensure that drivers do not freeze up when it does all go wrong (as it inevitably will at some point in a drivers life).