"The canonical link of Gamma GLM is $g(x)=1/x$ is often not very practical. Log-link is more appropriated in most cases." One reason I can think of is that log-link makes sure $\mu$, the mean, is always greater than zero. (please correct me if I'm wrong.) But I believe there are other considerations.
So why people often choose the log-link over the canonical one? Is it related to the fact that $\log$ transformation stabilizes data variance?