I didn't use HEVY after the first couple of testing missions. The main issue to me was the inaccuracy of the launcher.
I'm not sure if moving would decrease its accuracy, but well moving didn't decrease the accuracy of throwing at lease. A HEVY soldier in team generally has less than 40% accuracy when firing at long range, while a grenade thrower has more than 50%, in my own experience.
Also, the aliens didn't bunching up in most of the time, saving for inner UFO, in which scenario I would not use explosive anyway. Demo charge's much much better in destroying obstacles. So the usage of HEVY was narrow.