The answer is that up until then banks did borrow from each other when they were temporarily short of cash. Every day each bank reported to the Bankers’ Association the rate at which it had borrowed, the Association computed the average, and the whole world used that as their reference rate.
You immediately see the problem: if nobody is borrowing, there is nothing to report, and the rate on which international finance is anchored disappears. That is what has been the case since 2007, when commercial banks began to withdraw from the short term market for funds.