WWW -
Why on earth not? I believe it has got to come one day. Insurance companies change with the times. They always have. They even insure lighter than air craft these days - who would have thought it?!
As for press coverage, there is no howling by the press about: "Shock horror - Authorities allow pilots with only a few weeks of total flight time in little petrol powered planes to fly Jumbos!!!" (Maybe there should be!!) As long as precautions for safety are taken, and are shown to be taken, the press don't have a front page story.
Referring to Irish Steve's post, there would obviously have to be a restriction on the licence. If the pilot who is restricted to multi-crew, jet only, specific types then wants to fly for fun, he can get himself a PPL!!
Whether the current training system gives specific quantifiable benefits to large jet pilots, that couldn't be gained without flying small piston engine aircraft, is open to debate.
If any debate comes down, finally, on the side that there isn't any real benefit, or that the benefits aren't worth the time and cost, the world (and insurance companies) will adapt to the change.