A big reason for salt and other chemical deicers has to do with temperature.
In a lot of the Western states, yeah, they get a ton of snow all at once, but in a place like say Denver, they may get a foot of snow, but then it's 50 degrees the next week and a lot of it melts. In the midwest, we may get a foot of snow, and then the temps go down to zero for a week or two or three. If that happens, you end up with a nasty crust of ice on the roads and the only way to get it off is with some sort of deicer. Sand in the quantities needed for traction for weeks on a large freeway system would be prohibitively expensive and make a total mess of the storm sewer systems when they washed all that mud away.
Also unlike in the mountains, in most midwestern states, tire chains and studded tires are illegal and their use means a big big fine.