A screen protector can indeed protect your screen from shattering. Not that it absolutely will, but it can, much like the bumper of a car offers some extra impact protection for the cabin and frame of a car.
I'm meticulous about the care for my belongings, but accidents have that name for a reason - we don't plan on having a slight lapse in caution, but things sometimes just happen. My Nexus 7, with a glass protector, and in a case, slipped out of my hand and hit the sidewalk. When I picked it up, the screen protector was shattered but the screen underneath was flawless. Would it have been just as safe had I not had the protector? Maybe. But there's no denying that the protector clearly helped diffuse the force of impact.
And yes, it generally takes something harder than the glass to scratch it, so coins, keys, etc are not a big concern. But a single grain of sand... If it's going to happen, I'd rather it happen to the easily removable/replaceable glass protector (of similar hardness to the actual screen) than the screen.
As to cost, it's been my experience that the 'name brand' protectors in general are matched in performance by the $10 models you can get on eBay shipped from China. The only difference might be 0.1mm or so in thickness. Oleophobic treatment, fit, clarity are all on par.