Some landowners want it to be fly fishing only. The land owners control whether their stretches are open to the public or not. So it's best to keep them happy.
Also, many of these stretches are short, and very popular. Flyfishers can fish without moving very much, whether nymph, wet or dry fly fishing.
When fishing lures, that just doesn't work. Fish or either attracted to strike, or they are spooked by the flashy lure. Once you've run the lure through there once or twice, that area is done. So to be successful you have to keep moving, covering a lot of water, presenting the lure to as many fish as possible. The best spin fishermen fish miles per day.
And that is just incompatible with a stretch of stream with lots of flyfishers.