I think there’s some confusion over how contracting out government services works.
Government at any level can run a prison, seniors home, garbage collection, etc directly. Own the facility, pay the employees, out of geberal revenue (tax dollars) and such user fees as are possible.
Or they can contract out. They pay a lump sum to a private entity o run a service. The entity could be a nonprofit society or charity, or it could be a for profit corporation.
A for profit corporation contracting to do nursing homes or prisons will only do so if they can figure out a way to make a profit over and above all salaries and expenses. So they have a strong motive to cut salaries, cut staffing levels, cut services, and add on user fees. Many of these corporations are publicly listed, sell shares, and report their balance sheet annually.
They are making a profit because they are able to squeeze a profit out of the difference between what the government pays them and their expenses to run the facility.
The government couldn’t turn a profit on social services because they are the ones paying for it. The government might or might not be able to do the job for less than they pay the contractor, of course.
Similar to military contractors. They tend to do well and make a profit.