> ... to prevent silly mistakes like multiplying $100 with £20 Honest question, what should multiplying $100 with $20 give?
Hiring a better engineer for more money may create an efficiency improvement of 1 widget per dollar, with an outlay of $1k extra for the better engineer, giving a total gain of 0.001 widgets per square dollar; hiring a worse engineer for much cheaper may represent an improvement of 0.1 widgets per dollar, at an outlay of $1, giving 0.1 widgets per square dollar.
Perhaps not the most intuitive unit, but it's not impossible. (Though since you can even measure it in dollar-sterling if you like, I suppose that doesn't make it a counterexample to "stop multiplying dollars by sterling".)