Here’s why: because the Lannisters are noblemen and not merchants.
A couple quotes on this point:
“A coin is as dangerous as a sword in the wrong hands.“
His uncle Kevan looked at him oddly. “Not to us, surely. The gold of Casterly Rock …”
“… is dug from the ground. Littlefinger’s gold is made from thin air, with a snap of his fingers.”
Lord Tywin had always held the Free Cities in contempt. They fight with coins instead of swords, he used to say. Gold has its uses, but wars are won with iron.
Tywin Lannister was a very intelligent, well-educated man of his class, but that class was of a warrior aristocracy. He wouldn’t have been educated in more accounting than was needed to understand what his steward and his maester were reporting to him, because book-keeping is for women and servants. And that stuff is basic household accounts, not business accounting. And no Lannister would ever, ever learn finance, because that’s for merchants, and merchants are a lesser class of people who are concerned about gold rather than glory, who care more for probity than for honor. Look at how the Spicers are looked down on for coming from people “in trade.”
But I don’t want you to get the idea that Tywin was ignorant. It’s more about how he thought about money. Take a look at the essay I wrote about Tywin’s economic policy – Tywin’s father was looked down on because he loaned money to “common merchants,” even though that makes a ton of economic sense for the economy of the Westerlands, because it’s acting like a merchant. Tywin is a pretty classical mercantilist in a lot of ways – he wants to keep as much gold on hand as he can, because he thinks physical possession of gold makes you more powerful, he’s much more worried about getting his principal back than the income he might be forgoing in interest payments. And most of all, Tywin uses the gold of Casterly Rock for political purposes, not for economic purposes – he acts as Aerys II’s bank in order to make himself indispensable as Hand, he does the same thing for Robert in order to keep extending Lannister influence at court, etc. As the quote above points out, for Tywin, gold is a means, not an end in itself.
Tyrion, in part because he’s unusually well-read and perceptive, comes the closest to breaking out of this mentality, especially when he becomes Master of Coin and starts taking a really close look at the royal accounts. And even he, one of the smartest men in Westeros, can’t quite grasp what Littlefinger’s been up to.
And as I discuss in my “Who Stole Westeros?” essay here, Littlefinger is counting on this hole in the education of the Westerosi nobility to make his schemes work. Jon Arryn and men of his class don’t know about finance, so they wouldn’t think twice about what he was telling him about increasing revenues tenfold, and even if they investigated him, they wouldn’t understand what to look for.