They did it poorly. The past was rampant with organized crime that was fairly difficult to discover let alone trace. Modern accounting laws make it difficult to hide dirty money and help ensure that we have the tools to trace and collect evidence to take down criminal enterprises when we pursue them.

You also had a lot of tax fraud. It was easy to lie about things like how many children you had for tax discounts, so people often did. This particular loophole was closed by Social Security Numbers, but the principle is the same: records deter lies. The IRS often knows how much tax you should pay before you file.