Presumably if it dovetails back into the existing public court system at the prosecution level (i.e. there are railroad lawyers empowered to bring cases similar to DAs), that's still a reasonable separation of powers.
But the slope towards the government (with democratic checks and balances) ceding enforcement authority to a private party (without democratic checks and balances) seems worrisome.
With a very narrow space and scope.
The whole world is not New York City or the Bay Area where you have several billions of taxpayer revenues sloshing around you can throw at crime problems.
The "tough on crime" crowd needs to be less ideological and think deeply about the fiscal implications of taxpayers of their policies.
It all makes sense given that we are, after all, a former British colony. Great Britain’s whole thing with its colonial empire was to outsource its territorial defense to its colonial citizens.