Okay lets say that you're right.
That surface area of the collector doesn't matter.
I merely said that technical efficiency allows us to do more by using less.
This can conceivably allow any sufficiently advanced species to create technology which can focus massive amounts of solar power (for example) on a relatively small surface area and generate massive power from it (if proper materials and methods of production are used)... and the more advanced you become, you can generate the same amount of power (or more) on LESS surface area... and so on and so on.
Unless I'm mistaken, concentrated solar power does this very thing (and currently on a relatively large scale).
That increased collection efficiency over a radically smaller area of collection will still yield usable amounts of power for a starship.
Please clarify what you mean by this... because you seem to be in agreement that solar would create enough power for powering the entire ship, whereas we are mainly talking about powering replicators only while in the vicinity of a star (and I doubt that they would be the single most power intense piece of tech onboard - warp engines would probably be most intensive along with phasers which also focus large amounts of power to a relatively small surface area).
The power of a hundred atomic bombs per second restrained to a zone of a few square meters?
Shaped charges work in a way to focus the explosion and minimize the fallout.
SF technology was frequently shown to be able to focus massive amounts of energy onto single spots and even contain explosions.
Prime example of focused energy: Phasers (they ARE called 'directed energy weapons' after all).
Photon and Quantum Torpedoes could be considered pretty much shaped charges - depending on how they're configured.
Even in TNG, Season 7 'Emergence', the ship needed specific particles to complete the evolution.
Here's an extract from what happened:
RIKER: The ship is using a modified tractor beam to collect vertion particles from the star.
Why couldn't the same process be used for collection of solar particles for powering the replicators?
We're talking of a space faring civilization that has 360 years of technological advancements over us and travels faster than light.
Focusing massive amounts of power onto relatively small surface areas for the purpose of power generation would likely not present a difficult problem - especially when you consider the premise that something as small as a warp core also powers a pretty sizeable ship as well as everything inside it, while travelling faster than light.
These people evidently have no issue with the premise of 'generating more by using less'.
And this isn't just some special area of the universe, no, it's every cubed inch of space equally, even that which we are both in our respective corners of the world are sitting on is exactly that same destructive confluence of solar power as well...
Why aren't we dead?
I'm not sure I understand what you're asking here.
The Earth itself scatters incoming Solar energy as well as reduces its intensity by about 20 times.
Besides... you wouldn't have to generate 0.5 Zettajoules every second (which is what hits the Earth surface every hour).
With about 10 Zettajoules readily being available through 1 hour of sunlight in empty space... a SF vessel would need to simply position itself, collect and convert the said energy for immediate use - it would be like using the hull to maximize how much solar radiation each hull plate can absorb (which would probably be by orders of magnitude greater than what we can do), then convert this energy directly and transfer it to the replicators and transporters for immediate use... or heck, use it in the EPS grid and shut down the warp core to reduce antimatter expenditure.
Alternatively... the ship can use modified tractor beams to absorb solar radiation and use this energy for replication.
In every scenario, the ship would have to have a minimal amount of power to do the job... and if that's not available, then use a shuttle to act as a relay which will send you solar power that will charge the necessary systems long enough for the crew to replicate whatever they need and affect whatever repairs and resupplying are needed.
Heck... the lousy state of the Equinox would have probably been capable of doing the same thing.
