What makes the biggest difference in sound quality?

"When making changes or adding things to your system, what makes the bigger difference in sound quality on preamp‘s and power amps? Interconnects, speaker cables, power cords, or fuses?"

This possibly could have been phrased more clearly, but I think the OP meant that *of the options listed*, what makes the bigger difference. 

"And while power cords may make the biggest first impression, it is usually the last cable you replace, something like a mis-matched ethernet cable, an interconnect or a power cord going to something you don’t think matters, it is almost always the last cable that is perceived as making the single biggest difference when that cable completes the loom."

I think that this is the answer. In a highly tweaked system, it's the last thing you do that seems most significant, because all the previous improvements allow the most recent to perform at its best. Whichever order you upgrade your cables and fuses, the last one done seems most impressive. Or at least that's been my experience. 

As I learned today, I’ve been greatly underestimating the power of room treatments. I Installed a floor to ceiling bass trap in the most offending corner of my room and I’m astonished. Spent the rest of the afternoon recalibrating my sub to the “new room”. Best bang for the buck upgrade yet! 

As everyone has pretty stated everything matters and is important, but that is where i differ with most…

Let me go on the record as the outlier from the group with “everyone”.
Specifically with respect to the question of:
 

When making changes or adding things to your system, what makes the bigger difference in sound quality on preamp‘s and power amps? Interconnects, speaker cables, power cords, or fuses? 

I believe none of the crap matters much, and certainly not the power cords and fuses.

But I may be a robot, and I believe that I am passing the Turing test.

I believe none of the crap matters much, and certainly not the power cords and fuses.

Hearing aids work,  you should try one 🙏. 

The four items you mentioned, interconnects, speaker cables, power cords, fuses, all are passive components. They can’t add anything to the audio signal, they can only act as a filter and take part of the signal away.

Fuses and power cords are not in the signal path. Assuming they are well dimensioned to allow for the current peaks your amplifier asks, they can only help reduce electrical interference.

Interconnects and speaker cables are in the signal path, they can directly influence audio frequencies. On top of that, speaker cables need to have low resistance in order to deliver the current peaks your speakers require, assuming your amp is capable of delivering those.

I’d say of the four items you mentioned speaker cables can influence sound the most.

None of these four components need to be excessively high priced, just choose them carefully.