No, tension is what I meant.
Imagine the pile hammer hitting the top of the pile. This impulse is transmitted down the length of the pile at the speed of sound as a wave. There exists a point where the wave gets to the end of the pile (this is at the pile tip) and the compression front attempts to continue which results in tension (eg - the pile tip is dragging itself forward with the energy). This is mostly seen with soft soils where end reaction is not sufficient to provide a hard "stop" on the pile.
For hard ground, the opposite can occur where the driving energy reflects at the pile tip. This can result in huge compressive forces that crush (not crack) the concrete due to the two compressive waves (one new wave from the next hammer strike and the reflected wave from the previous hammer strike) stacking due to superposition.
The reason that this failure mechanism wasn't noted by me is that steel piles suffer the same issue, so it is not a good reason to use steel over concrete piling.
As you note, the solution to both issues is the use of a shoe and control of the hammer stroke.
I should have been more clear, I guess. Driven concrete pile is not used in the USA/Canada in my experience. When deep concrete foundations are used they are typically drilled in, for the reasons cited above.
There are obviously times when concrete piles are cheaper and will get the job done even with the risks above. This is most likely for smaller buildings where loadings are relatively light and pile lengths are therefore short.