"The capital investment to electrify cannot be justified."

To say that the capital investment required for electrification of selected US rail lines to electrify cannot be justified is a very bold statement without doing an in-depth return on investment analysis (ROI), which I doubt you have have done, almost certainly not at current fuel prices.

And if BNSF were to do an analysis showing an appropriate ROI, given Warren Buffet's (and Berkshire Hathaway's) involvement and resources, there is no reason funds could not be made available. Of course, a project like this would not happen overnight.

And there are privately owned electrified railroads built and operating in the US. Deseret Western and the TXU Monticello operation are 2 examples.
They weren't built because someone liked electric trains. They were built because the ROI was the best choice of the various alternatives to get the job done. Sure they are coal only lines run by utilities, but so what? If electrification was prohibitive, they would have been built as diesel. Now that diesel is several times the [former] price, they look even more attractive.

In round numbers, BNSF buys about 1.25 billion gallons of fuel a year. Assume $4/gal price, and the fuel bill is 5 billion dollars a year. That kind of annual recurring expense, (with little prospect of the price significantly decreasing), could [ROI analysis required here] throw off enough cash to pay off electrification over a period of years.

I'm not suggesting that BNSF could eliminate all diesel fuel cost, or even most, that would be very unrealistic. But a smart Board of Directors would be asking pointed questions in this area and a thorough review of the subject would be required.