I completely understand the principle you are trying to communicate. But your assertion that "it doesn't matter" is false.
Please consider the following:
If it is true that energy accounts for 100% of the price of everything, then raising the price of energy via a tax absolutely would alter the price signal by increasing the price difference between products with low and high energy requirements.
In overly simplified terms, imagine apples from Chile require 5kj to produce and apples from California cost 3. Imagine 1kj costs $.10. So apples from Chile costs $.50 and apples from California cost $.30. What happens if we add a $.05 tax on each kj? Apples from Chile now cost $.75, and apples from california cost $.45.
Makes sense?
It should also be noted that most proposals for energy taxes are on certain forms of energy, i.e. you'd levy a tax on carbon-based energy but not on solar energy. This would absolutely impact the signals sent by pricing.
No, your numbers don't make sense. The percent difference between the items is identical and did not change.
Please do not make the error of comparing absolute difference in prices, because that is not how money is compared.
The biggest problem with energy taxes is that when you increase the cost of energy, you also increase the cost of building a solar power station. So you can never catch up.
If solar power was cheaper than hydrocarbons, then no tax is needed, people would use it on their own.
If on the other hand you add tax, then solar power stations become more expensive to build, so they have to charge more for the energy - so much more that tax does not help them.
Please consider the following:
If it is true that energy accounts for 100% of the price of everything, then raising the price of energy via a tax absolutely would alter the price signal by increasing the price difference between products with low and high energy requirements.
In overly simplified terms, imagine apples from Chile require 5kj to produce and apples from California cost 3. Imagine 1kj costs $.10. So apples from Chile costs $.50 and apples from California cost $.30. What happens if we add a $.05 tax on each kj? Apples from Chile now cost $.75, and apples from california cost $.45.
Makes sense?
It should also be noted that most proposals for energy taxes are on certain forms of energy, i.e. you'd levy a tax on carbon-based energy but not on solar energy. This would absolutely impact the signals sent by pricing.