As for the corruption bit, with private security forces we know the weakness from the historical example already. With public police, public oversight puts a limit on corruption, at least in theory. Certainly London saw an improvement with the government providing police service.
30 years is a long time. Is Iran-Contra still on everyone's minds when it comes to discussions over geopolitics? I suppose it's still a factor.
I don't think the timescale was the same in 18th century England, but we're still talking about a generation-level gap here--I don't think you could just automatically assume a connection without some evidence.
Government police forces are policed by the government.
Private police forces are also policed by the government, but since they're different organizations, perhaps in reality it would be better.
One might be tempted to comment on the irony of your chiding "Libertarians" [NB: TFA is of unionist if not Marxist perspective] for their poor history, if one were not distracted by the implication that "entrenched corruption" is a rarity in the current regime.