Driving in snow and ice?

I think you're right on this.. And that's why the top tier winter tires are so expensive : they really try to mitigate the choice of compromise to offer the best balance possible... That's R&D for you people

 

Some test results for nordic studless tyres from finnish car magazine:

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First chart is road noise, second chart set acceleration, braking and handling test on ice, third set the same on snow, fourth braking on wet/dry asphalt and handling on wet, and last three are slush planing, rolling resistance and fuel consumption in litres per 100 km.

They had wider version of R2, "mild" winter tyre Conti TS850 and studded tyre (nastarengas) in this test for comparison. One important thing to note about studs is that they work well while new, but as tyre wears and the crown of the stud loses it's shape the difference to studless tyres decreases.