I think it really comes down to this:
1) The amount of force that can be generated in an elbow or a knee strike is very high in comparison to that can be made from a punch or kick.
2) Elbows and knees are real compact weapons that can be utilized in the clinch and on the ground. Because we know that a grand majority of fights are finished either on the ground or carry on throughout a clinch type of situation, this makes the techniques quite viable in MMA situations.
3) It doesn't take a large amount of training to learn how to effectively throw an elbow or knee. However, it does take a lot of training to learn how to control your opponent properly to make proper use of a well thrown elbow or knee.
What must be kept in mind is that although elbows and knees generate a lot of force, they are no where near as precise as throwing a well placed punch or kick. Because there is a larger striking surface in comparison to your fist or foot (base of the shin in MT style kicks), the force is dispersed over a larger area. It doesn't transfer into one focal spot. This is where you will see large amounts of damage dealt through an accumulated amount of elbows and knees, but one well placed, clean punch or kick will do dramatic amounts of damage (shot to the chin, floating ribs, liver, etc). In which case, accuracy definitely favors punching and kicking.
The problem with most "knife-hand" type strikes is that they need to be applied at just the right point or target to be effective. In which case, being able to rely on them consistently in a stressful situation doesn't lend itself well to those types of strikes. Further, a lot of the targets that you would attack with a knife hand (i.e. throat, base of the spine, neck, eyes, etc) are not legal areas in MMA competition. That would probably answer your question as to why they aren't as popular as you may expect.
I'll start a thread on how to throw an elbow in the stand-up technique forum. Hopefully, that can answer some of your other questions.
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