One is "What is the relationship between accounting and dead-reckoning logs as kept by ancient sailors?".
Another is "Why do accountants denominate all their accounts in cash?".
I think I have a possible answer to the second. It has to do with some contingent facts about business, which have been stable for so long that they seem to be necessary.
In business, you have various stores of value, and generally you have a "metabolic cycle" or "value cycle", which (if you're a going concern) is, in essence, over-unity. This is Marx's MCM, but it's more complicated if you are trying to investigate a specific business specifically; you might rent a truck and hire a driver and buy gasoline and maintenance and then exchange a promise to pick up and drop off a load at certain points for another promise to pay, and then go to the start point, exchange a receipt for a load, go to another place, exchange a load for a receipt, and then exchange the pair of receipts for money.
In most of your stores of value, there is a carrying cost. If you own a truck, then you're vulnerable to a novel risk of your truck being stolen, or breaking down, or trucks in general being made illegal, or something. Therefore, as you grow (over unity remember?), you're probably not going to want to spread your value evenly among your various stores of value. Instead, you're going to want to minimize your "work in progress", and put most of your growth at the store of value with the lightest carrying cost.
Cash (or cash equivalents) is generally the store of value with the lightest carrying cost. In unusual real world situations, something else (barrels of oil?) might be the store of value with the lightest carrying cost, the one that as you grow you want to keep most of your growth in, and so you might want to "recognize revenue" when you complete a cycle from barrels of oil back to over-unity barrels of oil. In other situations (a trader in the USD/EUR currency exchange market?), your "utility" might be a combination of two stores of value.
That is, the accounting has ALWAYS been in units of utility. It's simply an artifact of the historical / contingent fact that businesses want to keep their growth in cash, that accountants denominate accounts in units of money. If you want a new accounting, trying to grow something other than money, you can still use a lot of existing ideas from accounting. For example, if you have an uncertain venture, you might put the potential downside into your balance sheet immediately, and only if and when it pays off, cancel it out.