Implantable cardioverter defibrillators are expensive, and there are occasional false discharges (implantable defibrillators discharge relatively high energy, and the discharges can be painful for the patient, but not more than with a regular pacemaker, which is basically unfelt), and other problems are similar to those of implantable medical devices in general, which are kept away from places that can interfere with their work.
If a patient is really at risk of sudden death due to a particular type of arrhythmia, the benefits of implanting such a device far outweigh the drawbacks.