The power fist is so large and heavy, not just because of the power-field generators built into it, but because of all the heavy-duty hydraulics used to strangthen the crushing power of the fingers. If you were to take those out, all you would have is power-fielded fingers, which are not as effective as the alternative (lightning claws). The hrydraulics are where the strength bonus actually comes from, as even with a strong power-field weakening tank armor, it's still tank armor. One should be able to use the additional unnatural strength modifier without the power field, but only when one is using the fingers to crush something or tear it apart. The strength bonus should not apply to overall arm use.
Ex 1: There is a small gap in a ruined bulkhead. You can tell that there are flammable materials leaking over everything on the other side, but it's your only feasible route of escape. The Techmarine is unconscious, and there's not enough time for the Apothecary to revive him, so you can't make use of his servo-arm. The only option is your power fist. However, activating its powerfield greatly increases the risk of setting off the flammable material. Logically you should be able to tear and twist the edges of the gap with the hydraulic might of your powerfist without needing to resort to using the power-field (though it would certainly expedite the widening of the hole).
Ex 2: Your Battle-Brother is pinned to the ground by a large peice of debris. Your power fist may help break it into more manageable chunks, but cannot add its additional strength multiplier to lifting said chunks, and due to its prodigeous weight, should actually work against you, adding a negative madifier to the Strength test. (This should not apply to those using a power fist with Terminator Armor, as the Tactical Dreadnought harness should not only provide a stable platform for the lift, but the rerebrace for the arm with the powerfist would reasonably include additional hydraulics to further facilitate the use of the weapon. Come on, it's Terminator Armor).
As for using another melee weapon in the same hand as a power fist, well, let's look back at an example from the novels:
In the second Night Lords novel, Blood Reaver, the Red Corsairs stormed the Fortress Monastery of the Marines Errant. When they breached the reliquary, Huron Blackheart grabbed one of the two-handed relic power-mauls in his power claw, and stove in the head of one of the reliquary guardians. The power-field for his claw was inactive, and so was the powerfield for the relic maul.
One could use a melee weapon in the power fist-hand, but it would, by necessity, need a long haft that a power fist would be able to firmly grasp (meaning no swords, unless the grip is for two hands). One could not make use of the power fist's power field while doing this or they would destroy the weapon, and they would not be able to make use of any of the special qualities of the weapon being wielded (an Eviscerator wielded in such a manner would be little more than a barbed club). Additional negative modifiers would have be applied, as this set-up would go beyond unwieldy.
This is possible, but would be incredibly stupid to use outside of emergencies, or, in the case of Huron, humiliating the enemy with the inevitability of your victory.
Also note how huron caving in someones skull with a powermaul does not prove that a powerfist adds str bonus to other weapons damage, it only proves that someones skull was hit by a power maul.
If you disagree, please cite an actual place it says a normal powerfist has hydraulic strength amplification. And if it did, don't you think it would add to your score, you know like other things do that are meant to add strength, like power armor and manipulator mechendendrites?
Then there is the mechanics of it. Have you though about that? Have you punched someone before? The strength behind the hit has nothing to do with the strength in your fist. So it adding damage because of an extra strong fist is kinda silly. Punching something with a destructive energy field so strong it rips tank armor apart makes alot more sense. In your examples a manipulator mechendendrite would be great, but a powerfist is not that.