The main issue with Hellions that can fire on the move is with their AoE attack.
The flames currently last for about a second. If during that time, any unit that moves under the flames also takes AoE damage, then it becomes very easy to turn a linear AoE into a triangular area AoE. For example:
Let's say that "H" is a Hellion and X is the unit it's targetting (U is some other unit). Given this positioning, when it starts firing, it will hit X and 2 Us.
As it currently stands, if the Hellion starts moving, then the flames stop. However, if you have fire and move, then you can do much more damage if you shift the Hellion to this position:
That will cause it to hit X and 4 Us. That is an almost a doubling of the damage that the one Hellion did.
Imagine a block of Marines. Now imagine just
four Hellions that can, by sweeping their flames, do damage to
all of them. That is, each Hellion hits each Marine. In order for this to not insta-kill these Marines, Hellions would have to do less than 10 damage each.
Having such a low-tier unit be such a powerful counter to anything that travels in groups is not a good idea.