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The keys in the Wiki article are it tolerates hard weather and poor soils better than other small grains. Think the northern areas where rye breads are traditional. Of course, modern plant breeding and farming practices have changed some of that.
Here, rye was and still is grown in marginal areas or fields, mostly fields where costly inputs don't pay. Most livestock don't like it though some rye can be blended into their concentrates. It's used extensively for winter cover crops because it will germinate and grow even when planted in cold weather after fall corn and soybean harvest.
Horse farmers, especially the race horse crowd, like long straw for bedding, uncombined rye cut and bailed at its tallest just as it forms grain heads brings a premium price. Wheat and barley stems have been bred shorter and stockier to hold up under heavy loads of grain, old varieties of rye grow taller than your waist.