When people compete on their horses, it becomes easy for fads or the need to 'stand out' to the judges to replace the basic riding underneath.
Western Pleasure was supposed to show how a person's horse could be fun to ride because of its controlled, relaxed gaits.
My mare could never do WP...she's an excitable, snorting Arabian. But her jog is a great slow trot. Covers the ground faster than a walk, but in a very smooth, floaty manner. When I'm walking her, and she gets a bit nervous, she transitions to an even slower trot. If I'm leading her, she trots with her head at my shoulder as I stroll along. From her back, I'm pretty sure I could drink a cup of coffee while she does it.
In theory, it would be a perfect WP jog - slow, very enjoyable to ride, very comfortable - but her head is up and she may add a few snorts just for effect.
We're working on cantering. Her extended canter is too fast for the space I have to work her, so I'm trying to get her to slow down at a canter. When she does, she actually covers ground quickly, but in a very smooth & collected canter. Her relaxed canter is too fast to win in WP, but in theory it is exactly what a WP rider should want - very comfortable to ride, showy, and just plain fun.
In some ways, she would also be a good fit for dressage. She actively seeks interaction with her rider, and is the only horse I own that likes to be ridden without slack in the reins. But she would never tolerate having her head at the vertical. And there would be a high probability that in any given competition, she would decide part way thru that she needed to get rid of her stress by RUNNING!
I doubt either WP or dressage would approve of a horse bolting, and running 3-4 laps at full speed because life is exciting!
However, the basic riding style of WP & dressage seems very similar to me, possibly because it is meant for a collected horse moving in an arena. It isn't a style meant for covering a lot of ground, or moving along a rocky trail. It isn't meant for roping a steer, or jumping a fence. But in theory, at least, both WP & dressage riders should be having fun riding a collected horse under complete control of the rider - so it makes sense that, if form follows function, the form should be similar.
Of course, I ride neither, so I'm sure those who do compete can find fault with my outside opinion...