What's wrong with cathode followers is they don't clip nicely, if you're ever of a mind to clip something. They splat instead.
This shouldn't be so. The big problem with CF is that many designers think that, because they have a low output impedance, they are capable of driving low impedances.
A common cathode stage's output capability for positive output is limited by the current the plate resistor is capable of delivering; almost everybody understands that. Most of the times, the plate resistor is 100-200k and the output impedance is 50-100k so nobody expects it to drive low Z.
CF has the same limitation, except it's the negative output that clips. With a 100k cathode res, the output impedance is about 1k, but the quiescent current is the same as the CC, so clipping will be almost identical. Failure to understand that has led people to think they could drive low Z with 1mA quiescent current in the CF.
I must say also some designers are guilty of the same overlooking.