Do providers some how document there income. I would think they must to do things like get credit cards and home loans or rentals

Many of them run their business as a business, and report income and file taxes, and have retirement plans, medical insurance, investments etc. Others run it completely "under the table"

Most the smart ones I know pay taxes just like real people!  

and the pimp takes care of the rest, but only after beating the shit out of them first.  

Some times the boyfriend / hubby does take care of those things.
Few use a cover occupations such as stripper / counselor, and what not
but some just claim to be self-employed without any excuses or a cover occupation.

But seems that quite a few have a real day job where they don't need to report the income from escorting.

I would assume most have school or other jobs they also work.

most folks in a cash biz report about a third of their income, cant imagine its any different here

Any intelligent woman building a life and secure future for herself is doing that.  

That means depositing money into bank accounts and paying taxes.

The system doesn't care HOW you earn your money,  it cares that you carry your responsibility as a citizen of society.

Law Enforcement is a whole different animal onto itself. Unless you're running a huge agency that is enormously profitable, income  by itself won't raise flags.

So if you pay a lady over 600.00 in a year, you need her to fill out a W9 form and send her a misc 1099 form and report it to the gov.  W9 form needs full name, address, and TIN.   Yes, I'm the lucky guy at work that runs the yearly 1099 reporting process.  Please see IRS publication 1220 for full details.