Yes, and fiction is such a good indicator of what works in the real world...
I think we ought to differentiate or at least acknowledge that "privatization" can mean several things.
1. Gov't Contracting
Some level of gooberment contracts out to a private company to perform police functions. Very similar to what many cities now do with trash collection. The usual upside is better service at less cost and fewer gov't drones on the payroll. The big question is if the company's employees get all the authority of LEOs or operate under the same rules as us peons.
Are you sure?
That sort of thing has been (and is being) done a lot in the UK at the moment, with utilities, transport, refuse collections, school catering, traffic wardens, and many other formerly government-run services.
And in many cases results in things being costing more, and often being done worse than before. (Especially in the case of transport, where there is no longer overall coordination between the services).
Basically, because under the old system, the government payed for the materials and for the wages of th construction workers. Now, the government pays for the materials, the workers' wages, the company managers' salaries/bonuses, the shareholders' dividends, etc.
The worst examples seem to be the recent so-called "Public-Private Partnership" schemes used for building new hospitals, schools, etc. Formerly, these things were usually built by government-employed constructors, and then belonged to the government. Now the government pays private companies to build them, who then own or part own them, and the government pays them back over time, with the total coast ending up much more than before. The only beneficiaries seem to be the companies, who make loads of money, and the government, who create the illusion that spending is going down (because the up-front payment is less). The losers are the taxpayers, especially those living in the near future, who will have to pay balance.
In my opinion, the free market is
generally a very good thing. But the government taking my money, and spending it on services or construction projects of its choosing is
not a "free market". (Even if the companies themselves are private businesses competing for government contracts).