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Some key insights from the article:
Basically, what they did was to look at how much batteries would be needed in a given area to provide constant power supply at least 97% of the time, and the calculate the costs of that solar+battery setup compared to coal and nuclear.
No, LCOE is an aggregated sum of all the cash flows, with the proper discount rates applied based on when that cash flow happens, complete with the cost of borrowing (that is, interest) and the changes in prices (that is, inflation). The rates charged to the ratepayers (approved by state PUCs) are going to go up over time, with inflation, but the effect of that on the overall economics will also be blunted by the time value of money and the interest paid on the up-front costs in the meantime.
When you have to pay up front for the construction of a power plant, you have to pay interest on those borrowed funds for the entire life cycle, so that steadily increasing prices over time is part of the overall cost modeling.