Interesting interpretation. I've found it simpler to think in terms of using power, but energy being a relative metric. A conductor might be energized to a particular energy level, but completely useless unless a circuit is completed to a different energy level, thereby allowing power to be produced. The energy is neither consumed nor created, but merely converted from Chemical to Mechanical to to Electrical in a typical petroleum fired electrical generator.
With respect to simple algebraic equations, I've found it more productive to intuitively grasp the metrics of Maxwell's Eqns in differential format used simultaneously with some insight of 2nd rank tensors to better understand what is implied or generates one term from the other.
When you say "interesting interpretation", which of the numerous things I mention are you talking about?
When I mentioned energy, I was talking about energy delivered to the customers. 'Consumed' in the layman's terms but converted, as I mentioned, in more scientific terms.
You used the term 'power to be produced'. That terminology is where I have the problem. I would say energy is produced (converted) at a certain rate. You can think of 'using' power, but the only way you can purchase it is by measuring how long you use it. That is why the electric bill mentions the number of kWh you use. They could send you a graph of the instantaneous power versus time and show you the area under the curve, along with you peak power, but they can't charge you for power alone. Instantaneous power is interesting since we can 'see' what is going on and it does measure the stress on the delivery infrastructure, but energy delivered, (the area under the curve) is what we buy.
As far as being more impressed by current or current density, since current density is current divided by area, there are several ways to increase it. If we are looking at the main transmission line alone, the area of it will remain roughly constant, so quadrupling the current will quadruple the current density. I am equally impressed.
When someone proclaims a new power record, the public does not realize what it means. They don't realize that that record may have existed only for a few minutes. It does not necessarily mean record energy production (conversion) for the day. That is where the media lack of understanding distorts reality.
I am glad Maxwell's equations are helpful to you but they don't help the average guy trying to figure out the difference between power and energy.