Studless snow tires can still grip ice. For example, Blizzaks have "Bite particles for impressive traction on ice", plus sipes and special rubber compounds that wick water off the surface of the ice (the opposite of how ice skates work). Think of the bite particles like sand but in the tire instead of on the road. The sipes also provide additional edges to bite the ice if there is any texture or grit trapped in it. Studs are probably still better on ice, but studless snow tires are better on every other winter surface (including dry) and still better than all season tires on ice. Slick ice is not too common if road maintenance crews are doing their jobs, and I avoid driving in really icy conditions as much as I can because all it takes is a few people doing it wrong to make it dangerous for everyone.
Winter tires have to do so much. It's not as simple as just holding snow to grip snow. For example on slush they need to push the slush out or you'll hydroplane (slush-o-plane?). Same in water which you might find near melting snow piles in the winter. The also need to grip dry pavement when it's cold. And there are about a million different kinds of snow conditions depending on the temperature and how packed down or traveled it is and what shape it was when it fell out of the sky.
40 degrees would be hard to drive on on pavement, let alone ice. It's really steep! You probably won't find more than 20% grade even on most very steep roads, and that's only 11-12 degrees.
It's unfortunate the tires are so expensive. I can't justify the cost of winter tires because I always have the option to stay home if things get really bad, and I haven't had any major problems with all season tires as long as they have plenty of tread. In my last car, a 2WD sedan, I was sliding all over on about 4/32 of tread before I got new tires. On new tires it was fine and I never got stuck. But winter tires pay for themselves if they help you avoid an accident. I think most people have to budget for new tires, and no one wants to replace tires while there's still life left in them even if they aren't good for winter anymore.