Energy weapons are already too powerful, there is no need to give them even more versatility by allowing players to supercharge them at the penalty of greater heat, it simply encourages hit and fade tactics even more like pop tarts that jump, alpha strike, shutdown mid air, and land behind cover to cool off.
There are two different penalties in CBT applied to movement, one of them I don't think the mechwarrior games really accurately portray.
There is enemy movement, which is based on the speed of the enemy mech. This is handled fairly well, especially with having to lead targets with PPC and ballistic weapons.
Then there is your own movement, which boils down to stationary, walking, running, and jumping.
Stationary applies no penalty.
Walking is ~66% of your maximum speed and applies a +1 penalty, equivalent to firing at a target moving ~30kph
Running is ~67+% of your maximum speed and applies a +2 penalty, equivalent to firing at a target moving ~50kph
Jumping is, well, using your jump jets, and applies a +3 penalty, equivalent to firing at a target moving ~70kph
This is what I'm talking about with having "weapon sway" or just a really bumpy ride. Think of most FPS games now-a-days. If you try shooting your weapon while running and jumping, your cross hairs get HUGE and your rounds could fly all over the place inside that expanded area. If you drop prone your cross hairs get tight, and your accuracy increases. In mechwarrior, however, your cross hairs never shrink or bulge, but they should, it's a big walking man-shaped machine. It has certain physics like hip, arm, and torso sway in order to keep balance, especially at high speeds. Your weapons should suffer some accuracy issues while running, or, especially, jumping, such that even hitting a stationary target is no longer "easy".
It is this factor that makes assault mechs friggin' scary in the tabletop. They have the armor to sit stationary and blaze away at a light mech, while that light mech MUST keep moving at maximum speed just to stay alive, thus making it more difficult for the light mech to land shots into the assault mech.
This is the strategy that mechs like the Awesome were designed for. They find a defensible position, and stand on it, and blast away with their PPCs at anything that gets into range. The only way to dislodge them is to get closer, and that requires enemy mechs to close range, preferably fast mechs so they don't get torn to pieces. But fast mechs are generally light on armor and armament, so even when they get into range they aren't making mincemeat of the Awesome. This is basic CBT strategy.
Now, there are game balance issues at work here. Throw them out the window. The balancing factor is C-Bills. An Awesome should destroy a Commando. Gunnery skill might dictate that the Commando lands a few more hits, but there is little a pilot can do to stop the inevitable PPC massacre coming his way. This is akin to putting a Humvee up against a MBT. There is a reason the MBT costs excessively more than the Humvee, because war isn't fair.