Olympic weightlifting from my perspective has a higher entry bar than say powerlifting or bodybuilding which is why I believe that Olympic weightlifting is less popular.
Americans
In America, there no exposure of Olympic Lifting when growing up.
Kids grow up playing American Football, Baseball and Basketball for the most part.
Other Counties
In countries like Russia, Bulgaria, China, etc., Olympic Lifting is like American Football; it's a popular sport.
The average person may not appreciate the biomechanics and technique of a clean and jerk without first knowing them.
The Average Person In America
The average person in American is clueless as to what Olympic Lifting is. They often don't know the difference between Powerlifting and Olympic Lifting.
Ironically, the majority who do train with weights refer themselves as Weightlifters. A Weightlifter is is another term for an Olympic Lifter.
With that said, it hard to have any appreciation for something you are have no understanding of.
...do you believe that Olympic weightlifting has any carryover to powerlifting or bodybuilding?
Carryover
There definitely a carryover of "Olympic Movements" to other sports like Powerlifting and Bodybuilding.
Olympic Lifting
The Olympic Lifts are Power Movements.
Some of the highest, if not the highest movement recorded are the Olympic Lifts/Movements.
Conjugate Training
Olympic Lifters are the Poster Children for Conjugate Training; combining Maximum Strength and Power Training.
Chinese Olympic Lifter are no incorporating Hypertrophy/Bodybuilding Training into their program, as well.
The Westside Powerlifting Conjugate Protocol
The Westside Powerlifting Method incorporated Maximum Strength, Power (aka Speed) and Hypertrophy Training into it program.
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Power Training employs the Squat, Bench Press and Deadlift with load of 48 - 62% of 1 Repetition Max. This training percentage with Traditional Strength Exercise develop Power but not to the same extend as True Power Movement like the Olympic Movements.
Research (Dr John Garhammer) determined that over 4 times as much Power Output (measured in watts) was produce with Olympic Movement compared to moderate load with the Powerlifts.
Dr Michael Zourdos
Zourdos' (Powerlifter) research determined that a Conjugate Training Program that involved Hypertrophy, Power and Maximum Strength Training in the same training cycle increased Maximum Strength.
Dr Brad Schoenfield
Schoenfield's research determined increasing muscle mass was best achieved with the following...
1) Mechanical Tension: Maximum Strength Training
2) Metabolic Stress: The Bodybuilding Pump.
3) Muscle Damage: Pushing to failure or near it. Additional research (Dr Jake Wilson) found that full range movements (like Squat) produce muscle damage that lead to an increase in muscle mass.
While there no direct research that indicates Olympic Movements is effective for Hypertrophy Training, it appears that some type of Power Training may assist.
Dr Jonathan Oliver
Oliver's research involved the use of Custer Set Training as a means of increasing muscle mass.
When Traditional Hypertrophy Training ONLY is used, Power and Maximum drop like a rock.
Oliver Cluster Set Hypertrophy Training demonstrated that muscle mass was increased along with Power and Maximum Strength
The underlying mechanism is Cluster Set Training specifically trained and developed the Fast Twitch Muscle Fiber; the largest muscle fiber.
Olympic weightlifting could still be considered a niche with the exception of the clean and press which has grown in popularity due to the likes of Crossfit and Supertotal.
C
rossFit and Olympic Movcements
The Olympic Movements have increased due to CrossFit.
Unfortunately, many CrossFit instructors lack the knowledge to correctly teach these technical movements.
CrossFit often employed them for Metabolic Training, which it does.
However, when using the Olympic Movements for Metabolic Training come at the expense of developing poor technique, increasing the risk of injury and decreasing Power and Maximum.