There are actually muscle cells that have given up the ability of contraction in favor of conduction of excitation. If such a stimulation conducting muscle cell fails, the neighbouring cell can immediately take over the stimulation conducting function.
If only nerve tracts (axone) were present for the conduction of the stimulus, the heart would not be excitable for a long time after its failure, which would result in immediate death. The same applies to the sinus node, which can be newly formed in the event of a ectopic failure.