1. Why doesn't every single Mazda 6 owner (in even marginally snowy areas) switch to snow tires each winter?
2. Which ones do you recommend?
FWIW, I'm in NY Tristate, with a 2015 Mazda 6 Touring
Change that to "why doesn't ANY driver in ANY vehicle where it snows" and I'm with you.
Most people these days (modern so-called "all season" tires) have NEVER driven a car with snow tires in the snow. Do it just once and you'll never not do it again.
I grew up before there was such a thing as so-called "M+S All-season" tires. I put snows on when the first snow was seen and on they stayed until it was gone. It's a huge difference.
Buy a set of STEEL wheels too. Your nice wheels will thank you when you hammer a big pothole (caused by said ice and snow!) and don't destroy said nice wheel. The steelies are cheap and MUCH stronger. Oh, and 17" please -- it's idiotic to run low-profile snows (do they even make them?)
The only serious issue is where you store said set of tires and wheels in the summer. If you have a garage, no problem. If not that be a material problem. But it's one you really do need to solve if you live where it snows.