I would not make that statement for off piste. 2018-19 was an exceptionally banner early season through January at least for Austria and eastern Switzerland with repeated Nordstau storms. We scored that region a month after James did.
And you would not say that such events are more likely in December than in February/March? Larry Schick (who worked several years for Army Corps of Engineers) say almost all of the most destructive Pacific Northwest flood events have been between November and January. The rain/snow line tends to be lower in February/March so all that water isn't coming down in the immediate aftermath of the storm.
I have lots of data confirming the water vs. snow along west coast North America, but I've learned that analogies don't necessarily apply. Central Chile is a very obvious analogy, and there are aspects of its climate significantly different from SoCal's (cloudiness, heat extremes, rain incidence). So I'm sincerely interested in whether western Europe has the same rain/snow line incidence pattern as we do here.
I'll synthesize Fraser's and ChrisC's recommendations with my own two cents:
France
I agree with Fraser here. Precipitation in the whole northwest quadrant of the Alps is fairly tightly correlated. Even if that sector gets off to a good start at many places, the odds are high it will still be best at Val d'Isere/Tignes. That might be the difference between having adequate vs. marginal off-piste coverage.
What's less correlated are the resorts from Alpe d'Huez to Serre Chevalier and farther south. They are also less likely to be the right choices and are a longer haul from Geneva (and a full day from Zurich) in a year like this past one where they did have the most snow
Austria
I still like Austria for the slightly colder climate and comprehensive snowmaking systems to utilize it. And I agree with Fraser about Ischgl. Most of the ski terrain is above 2,000 meters and topography is heavily intermediate, meaning at least bits and pieces of off piste might be skiable in an average late December. In the long run, Ischgl will most often be the right choice in skieric's time frame if flying into Zurich.
But as always we say, don't commit the lodging until a few days ahead. The very snowiest resorts in the Alps (Warth, Damuls, etc., some of James' favorites) are in the leading NW edge of Austria. So they have a decent probability of intermediate off piste coverage, with the caveat that they are lower so you need to be sure their progress hasn't been set back by rain.
If the region gets lucky with a LOT of early snow, that's when you should consider the Arlberg with its excellent terrain quality, keeping in mind that you'll need more coverage to be skiing off-piste there. If you're going to be confined to groomers, I agree 100% that Ischgl is the superior choice.
Switzerland
I know ChrisC loves Engelberg and Andermatt, and we understand why as we were there with him in January 2019. But the experience at both places is highly dependent upon advanced off-piste terrain being covered. Both places have snowy reputations, but I'd still be skeptical pre-Christmas. I'd want direct and timely confirmations from an on-site off-piste guide service before considering either destination.
Zermatt is a fascinating place. Having skied it in its prime in 2014, I'd be frustrated looking at all that outstanding off piste too rocky to ski. Yes, it's scenic but if confined to on piste Ischgl and Val d'Isere are better.
Italy
If you are totally conceding the point that you will be confined to groomers, yes the Dolomites are worth consideration. As long as you don't mind what it will look like if there's minimal natural snow.
Worst case driving scenarios from Zurich:
Val d'Isere: 5 hours, 48 minutes
Val Gardena: 5 hours, 5 minutes