I have a different ideia that believe to be somewhat more logical, though the effect may not be as extreme, it should at least prevent large numbers of weapons being fired at the same time and make people think a little on how they should fire their weapons.
So imagine how the engine supplies power to the weapons around the mech's body, imagine how some weapons require more power than others, imagine the engine not being able to cope with the requirements of sending energy to all body parts (or almost) at once.
Lets suppose an engine is perfectly capable to sending the required energy to fire two PPCs, but its not just the engine that should be in the equation, but also the cabling and stuff between engine and weapon. So lets say an Awesome fires its torso PPCs, one is in the left, the other is in the right, the engine can handle it, both PPCs fire at the same time, no delay. Now lets say the awesome fires the arm ppc along with the torso, the energy route from engine to right arm is stressed due to ppc fire in right torso, extra heat caused by that, as well as delay in right arm ppc. (on a side note, I would sugest quirk to be added to the awesome to be allowed to fire all 3 ppcs without penalty due to chassis design feature, extra cabling or whatever, the awesome needs some love).
Another example, the Jaggermech with dual AC20 fit, big weapon should require more energy, firing two of them without penalty should only be allowed for bigger engines, and the Jagger shouldnt be able to have the required engine along with two AC20 due to not enough tonnage. So in this case, firing both AC20s should not necessarily cause extra heat as the power goes along different routes (unless you think of engine stress) but will cause firing delay of one of them, ammount of delay should depend on size of engine and its power output (PGI im sure could come up with some math and formula for this

Yet another example, you have a Raven with AC20? You probably cut on the engine to be able to mount that uber weapon on such a small mech. You fire the weapon, even although its just one, engine is not powerfull enough and becomes stressed, get a fire delay for that single shot you took, oops you missed the target.
Lets keep'em comming:
Hunchback 4P, all those medium lasers and a crapy engine, well the medium lasers dont take that much energy, arm ones would fire fine, but some of the torso ones would be delayed if fired all at once, and extra heat due to stress.
Stalker with 6 LL, 2 in each arm and 1 each torso, firing both LL of one arm would cause stress and delay, 1 from each location might be able to handle it, possibly depending on engine capability, not sure if that fit requires smaller engine.
I think part of the idea here is to influence people to make smaller weapon groups and fire them with some interval, or have high alphas cause extra heat AND weapon fire delay to mess up the pin-point fire.