I don't think most of those businesses realize that, in the end, they may wind up paying more in taxes by paying "off the books" than if they just did things right. This is because when you pay employees legitimately, you get a 100% write off not only on their wages but on all the taxes and other expenses you pay for them. When you pay these employees "off the books" you get zero deduction for the money you pay them, which means that it inflates your business income which, in the end, you will be paying federal, state, and local taxes yourself on the money you paid them because it can't be deducted. For example:
Let's say that over the course of the year you pay $10,000 under the table to workers. Of course you save on the taxes and other expenses that you would pay in addition to that $10,000. But, you can't write off the $10,000 you paid them so it winds up, on paper, making you look like you earned $10,000 more for the year in profit than you actually did and you have to pay taxes on that money yourself, as if YOU actually earned it yourself. To make things simple, let's say that you are in the 12% federal income tax bracket and guess that you pay 5% in state taxes. So, on that $10,000 that you couldn't write off, you wind up paying a total of $1700 more in personal federal and state income taxes than you would have if you had not paid under the table. So, that makes you $1700 in the hole in that regard so you better hope that the taxes and other expenses that you "saved" by paying these workers under the table actually adds up to more than that $1700. Many of these businesses who do that would be surprised to find out that they are actually personally losing money by paying under the table.