I take it you haven't done any home remodeling work lately? Businesses like plumbers _love_ cash, in the sort of amounts under discussion. Thinking it doesn't happen is just bizarre.
That's not paying the business, that's paying the person - it's exactly the same thing one step back. That cash won't appear in their business accounts. The whole purpose of paying them cash is to enable their tax evasion.
Simply false. In every case of my personal knowledge, and there are very many, it has been to protect the right to privacy, and no taxes have been evaded. I find use of cash in all amounts to be increasing as surveillance increases.