Starting a y-axis at zero has its advantages and disadvantages. Charts where the y-axis does not start at zero can exaggerate the differences between data point values and the steepness of the slope of connecting lines that might otherwise appear rather slight. In some situations this may be deceptive.
However, in other situations slight variation may have enormous impact (for examples, a single degree difference in global warming). If these small changes are significant to your story, it may make sense to not start the y-axis at zero.
Context should be taken into account, and choosing whether or not to start an axis at zero should be considered with caution.