Impossible, naw. Impractical, hard to say, maybe so. I never suggested a "heavy but stable" big mountain ski. And I was talking about a setup that could handle light, eg, day tours, sidecountry, groomers. I cast it as an issue of destination conditions, not habitual ratios of frontside to backside. As in, I'd like to spend five hours skinning near lift served, but the snow's crappy, so I decide to blast groomers. Or the reverse: I show up and it's just had a storm, the groomers get skied off fast, so I'm off to the OB for the afternoon. You see? Neither 6 day tours of Switzerland's huts, nor one run past the ropes, then back to the lifts and a beer. So I'd turn it around and say that most people who actually skin nowadays, rather than use a Duke cuz it's cool, only do so for part of a day, and are a more interested in the down than the up. But that doesn't mean they wouldn't love a tech setup that actually worked for serious downhill. The difference mechanically between a tech setup and AT is non-trivial; who wants to lift an entire binding every step if they could just lift their heel, and have a real pivot point where nature intended?
All that in mind, IMO there are plenty of comparatively light chargers out there. The Stormrider 107 comes in at 3960 g in 183; the 100 is a mind-blowing 3640 g at 182, and no one ever accused Stocklis of being twitchy in bad snow. Praxis makes some very highly regarded big mountain models that are under 3900 g. The Fat-ypus D-Sender is stiff, likes to go fast, and weighs under 3,800 g at 184. And if you like the DPS feel, well, couple to choose from that are stiff. ON3P or Prior or PM Gear can build you a fat stiff ski that comes in under 3900 g. The list goes on.
As far as DIN, not clear why preloads are less significant. The heels in a tech binding take the place of the toe. So a high DIN tech binding will be desirable because of the beefier heel springs, if the skier is a big guy (as in, over 200). Recall that F=Ma, so if a guy at 220 is going to charge heavy snow on the backside, he'll want both elasticity and the ability not to launch. Ever follow Thin Cover's travails over at TGR? He was about 220-230 at the time of his first accident, I believe, now about 240. And plenty of guys well over 200 there who do serious touring.