There seems to be a glaring incentive problem at the heart of all this.

What happens when a subscriber of company A commits an offense (let's put a pin in what constitutes an "offense") against a subscriber of company B?

Company B has a strong incentive to punish the offender, but Company A is disincentivized from having its subscribers hauled off by Company B. At a minimum, they lose the subscription fee; more realistically, the market will push toward police companies that protect their subscribers from rival police companies and successful companies will be like the US when confronted with an international court -- "we're not sending our people to that thing run by foreigners!"

This only gets more intractable if different private policing communities use different legal codes. Why would A hand-over its subscriber to B if the complained-of offense was "blasphemed against Odin" or "refused to acknowledge their White Privilege" or "had gay sex" or whatever thing you think is absolutely fine but someone else thinks is a crime? Or assume that substantive law is identical, but one jurisdiction allows for cross-examination at trial (wait, how does it compel witnesses to appear?) and another does not? Do you hand-over your subscriber to the latter suspecting that her trial will be fundamentally unfair (as you conceive of fairness)?