For me the reason was that I wasn't particularly happy with any of them. I wanted to modify some systems but never came around to it.
Variant 10 is surprisingly the most interesting one, I think the cooldown has potential.
HEF variant 1: all flux generated is hard flux, +50% damage
Good balance in a shield-up situation, but too powerful if they can stay down (if either you out-range the enemy or your armor is too thick for him, aka flyswatter mode). A standard Odyssey wont raise flux with HEF and shields down.
HEF variant 2: all flux generated is hard flux, energy damage bonus based on flux (50-150%)
interesting, but too hard to manage. overpowered since 50% basic damage bonus.
HEF variant 3: +50% range on energy weapons, +25% flux generated
boring. encourages staying out of range with shields down
HEF variant 4: beams get +50% range, other energy weapons get +50% damage, generate +50% flux
HEF variant 5: +50% damage, engines are disabled and ship slows to a halt quickly
Overpowered, almost no disadvantage for cruisers/caps.
HEF variant 6: +50% damage, halved shield efficiency
Totally overpowered
HEF variant 7: +50% damage, +50% flux generated
similar to variant 1
HEF variant 9: Energy damage bonus based on flux (up to 30%), range bonus based on flux (up to +70%), generates hard flux
In most situations this means that your range get greater if you go for a melee (to raise flux) where you don't need it.
HEF Variant 10: +50% damage, no flux dissipation, 30 sec cooldown
The cooldown is very interesting. It puts me in a conflict, I really want to keep my HEF on because it's so good and I can't use it again fast, but then I know that I should really turn it off now because my shields can overload any time. No flux dissipation takes that interesting decision away from me, though. So cooldown yay, no dissipation nay.
Maybe combine it with 1 or 7?
HEF Variant 11: constantly generates hard flux, 3% bonus to energy weapon range and damage per second the system is active, 10 second cooldown
This requires some weird tactic, hanging back and waiting for your system to charge. Don't like it.