I've posted the solution repeatedly, and have found this "feature" to be one of the stupidest things ever to come out of Paradox. (Sorry if that hurts anyone's feelings over yonder. I am a really big fan and supporter. I just find this system indefensible historically or simulation-wise...)
Anyway, the solution:
1. Privateers should be given a "Letter of Marque" -- a pop-up window which allows you to designate which nation(s)' trade they are going to be hampering. It should not be for "everyone in the node" -- unless you want to actually do that. Privateers were targeted towards specific nations. Say, France, or the Netherlands, or Spain. Or a short list, like "Spain and France." Not sent out to attack all-and-sundry. But hey, if you think you can deny trade to everyone, go do it! Flag against everyone else in the node. Just expect this to lead to conflict.
2. Privateering should indeed give a "Trade War" CB for anyone targeted by it. Such deprivations were not a "Mission Impossible" secret, where the secretary would disavow any knowledge of your actions.
3. Privateers should NOT come out of the standing navy, but should come from a sort of "mercenaries of the sea" stockpile similar to land mercenaries. This would represent the number of merchant marine captains who would be willing to undertake the hazards of being a privateer. The standing navies of these nations did not "reflag" themselves to become buccaneers.
4. Privateers would need to pay for themselves through the losses they take out of a trade node. If they cannot sustain themselves, then they should "die off" (go back to other commercial ventures) over time.
5. All targeted nation's ships should be able to attack the privateers (or be attacked by the privateers) without directly going to war with the sponsoring nation. After all, they are "hostiles" operating in your territorial waters.
This is what I have been arguing from the beginning. It is far more historical. It is far more competitive. It is far more understandable than the current "state-sponsored pirates with a Klingon cloaking device" that we currently have now.
Some things are good but others not as much.
The main problem is that ships here don´t operate like subs in Hearts of Iron, where they can or not encounter convoys, and can or not be attacked by fleets. Instead they are auto-detected. Result? Got 10 privateers in a node?
I send 20 and kill your fleet. So no - under the current naval system, you have to make ship destruction only possible by war. One solution that can be used is large ships decreasing privateer efficiency and even damaging them.
Also totally disagree they shouldn´t come from your naval forcelimits.