Idiots will get stuck whether they have winter tyres or not.
I can see the benefits of winter tyres and for a couple of years now have been meaning to buy some part worns but despite taking the royal biscuit the last few years in the snow, almost inviting myself to get stuck, I've not managed it yet, be it in the Corrado, VXR, BMW, Mondeo or Focus (all cars with big wide summer tyres). That said, the Yaris on 165/60/13s or something was absolutely incredible in the snow on ditch finders.
Long story short - winter tyres aren't some magic formula that let you drive in the snow like it's a warm summers day, so those getting stuck on "normal" tyres will still end up stuck on winter tyres.