Equity method accounting relates to GAAP financial statements. Dividends received (in terms of cash flows) from the investee would generally be taxable to Berkshire, reduced by the Dividends Received Deduction.

Quite right. I used an LLM to summarize the relevant tax code section. Its summary was flat out wrong, and I couldn't follow the description in the referenced page either : )

The reason that the dividend reduces the book value of the stake is pretty easy to understand...

Well, yes and no. Yes, it is logical in its internal consistency, but not at all intuitive in the sense that the booked value over time is no longer any kind of approximation (however flawed) of true value as most investors would expect. And also not intuitive in the sense that it doesn't resemble the familiar result from smaller shareholding percentages. The shareholding in a typical growing firm paying dividends over time will be worth more and more, yet its carrying value will lose its connection to that if the payout ratio is big. At first it seems rather like booking the position at the book value of the investee (earnings move it up and dividends down), but it isn't that either.

Jim