How strong are pedals?
What about other components of the pedal interface? The threads? The threaded insert in a carbon crank? How about the cranks themselves?

I'll use the &quot;pardo&quot; durability index to answer. The durability index is based on the number of failures at http://pardo.net/bike/pic/index.html.
For pedals, we see three failure events.
For cranks, we see 55 failure events.
So it seems based on this that the crank pedal eye fails far easier than the pedal connected to it.
One reason is that the pedal to crank attachment has a design flaw, and the crank, being made of aluminum, is the component that suffers as opposed to the pedal spindle made from steel, a far stronger material. The design flaw can be seen from the left pedal having a left hand thread -- a proper design would not be sensitive to threading direction. It can also be seen from old cranks, from which the removal of pedals sometimes is a Herculean effort and even when it isn't, the pedal eye of the crank is visibly worn. The pedal to crank pedal eye attachment should have a 45 degree taper, similar to automotive lug nuts.
Of course, non-catastrophic failures of cheap plastic pedals happen often. Those are used only in inexpensive bicycles intended for little kilometers in their lifetime, for light riding.