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.
You are wrong. The core book says so. Using huron blackhearts unique bionic arm as an example of how powerfists work is as silly as saying all lightning claws have built in combibolters because Abbadon's Talon of Horus does. The core book does talk about how the powerfield on a powerfist is far stronger than any other weapon's, so strong in fact that the weapon underneath is irrelevant. Let me repeat an important part, so strong a powerfield, the weapon underneath is irrelevant.
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. Making your fist real strong would be kind of silly, unless you were gonna make your whole arm stronger to. What was your strength fist going to do, squeeze things you cant lift? Have you reeaally thought about that hydraulic fist idea of yours?
Nothing you said made sense until I saw that you misunderstood me (or rather I didn't make myself clear) about strength bonuses in relation to wielding a melee weapon in the power-fist hand. No, there would not be a strength bonus to using a melee weapon in the power-fist hand. There would probably be a strength penalty, actually. The fingers can manipulate, but are not designed for such movement, so the extant unwieldy nature of the power-fist would stack with the clumsy grip brought about by the poor manual dexterity. It's one of those things that's possible, but not practical in any way.
Your comparison to Abbadon's lightning claw would only make sense if I was arguing that all power-fists have an integral heavy-flamer. I have made no such argument. The logical mechanics of the power-fist/claw with it's oversized digits should allow the ability to manipulate objects at greatly reduced dexterity. Especially when one considers that their fingers are not actually inside the digits we see. Seriously, look at the spacing on those fingers. Even with the size of the Astartes hand, to get a finger in each of those would require that the metacarpals be separated from one another surgically, so the hand is just a wrist-stump with really long, splayed fingers. The fingers on the power-fist are mechanical, either utilizing hydraulics or heavy servos ( http://img11.nnm.ru/...730e5fa01f5.jpg ) (Admittedly this doesn't address the comparable size of the lightning claws, and their lack of an additional strength bonus, but the upped the size to near-power-fist after 3rd ed for some reason I can't wrap my head around. Realisticall, at that size, they shouldn't move as fast as they do).
While the book says the weapon underneath is irrelevant, that doesn't seem to actually be the case, or it would just be a big heavy lump with a normal-sized Astartes gauntlet under it. The hydraulics and servos are described in reference to the power-fist used by Solun Decius in the HH novel Flight of the Eisenstein, and to the power-fist used by Chaplain Eysius in Firedrake. Sometimes punching with the power-fist is not the answer, and you use the hydraulic strength of the fingers in tandem with the power-field tear apart thick obstacles that cannot be taken down as quickly with raw impact force. While it may be reasonably argued that the additional strength multiplier is too much in this instance, some positive strength modifier should be applied.
I work out three times a week, and box at least once a week, and have for the past two years. I know how to throw a punch. Throwing a punch with a power fist is a completely different beast altogether. It's massive and unwieldy (which fists normally are not), shifts your center of gravity (which fists normally don't do), and cannot effectively be used for quick, distracting jabs (which fists normally can do). The power-fist is a big, heavy block of ceremite, power-field generators, and hydraulics/servos that is swung in the direction of the enemy. It would come with additional rerebrace hydraulics to ease strain on the elbow servos, but even a reinforced lever is only as strong as the material it is placed upon. The only time anyone's power-fist technique might be compared to throwing a proper punch would be in the case of Inquisitor Obadiah Roth in Emperor's Mercy.
Making the arm stronger, alone, isn't necessarily going to increase lifting power because there is a ceiling on how much the rest of the body can withstand. If you were to increase the lifting strength of your arm by 500 lb right now, would you be able to deadlift your previous record plus the 500? The answer is no. Not if you didn't additionally strengthen your shoulder, back, and legs. Not to mention the joint strain. Even if one takes a power-fist that is designed to enhance full physical strength A stronger arm does not automatically mean you can lift more, hence why I argued the penalty would not be incurred by one in Terminator Armour (as the rig is actually designed to support the power-fist, and provides a stronger platform for the arm).
My point is that they leave the fingers there for a reason, and that the massive size of them rules out being left there strictly for the ability to manipulate. Otherwise they would have normal-sized fingers, or they wouldn't have fingers at all.