In the original Library Data the first/lowest tier of Imperial government is the sub-sector Duke. They are tasked with seeing to the economic well being of the worlds within their sub-sectors, overseeing the deployment of Imperial resources, and ensuring that worlds pay their taxes.
Rivalry exists between sub-sector Dukes, they are competing for limited Naval assets, they are trying to encourage megacorporation investment within their sub-sector, and they are constantly striving to exploit the resources the sub-sector offers.
A sub-sector Duke who can encourage the development of a couple of high pop worlds, or a nice mix of industrial, rich and agricultural worlds, will have considerably more influence at the sector level - and may even aspire one day to that lofty position.
So how to stop your neighbours doing the same? What if a world just over the sub-sector border offers great trade potential?
Megacorportions are the power behind the throne of the Imperium. They exploit the resources, operate the refineries and factories, transport the goods to market. They conduct exploration - to find new markets and resources - they conduct research and development - to stay ahead of the competition, they found colonies, buy and sell whole worlds, and pay their taxes...
So what if a rival company is making inroads into your market share? What if a world that used to provide the raw materials for your factories decides to trade with someone else? What if an upstart transport company starts to undercut your transport monopoly? What if another megacorporation perceives your foothold in a particular region to be weak and ripe for takeover... hostile takeover.
Individual planets are free to govern themselves as they see fit. They are free to build their own naval ships, to subsidise trade, develop their own economies, exploit their own resources...
So what if a rival world has ambitions to claim an uninhabited part of your system, or you want to develop the potential in another worlds system because they lack the resources?
So basically I can see how each of the above groups would sponsor raiders within the territory of their rivals.
By claiming "Trade War" you have partial immunity from the IN blowing you out of space because of your activities. The letter of marque is a natural extension of this IMHO.
This helps me to explain three things:
how the pirate career can have such a well defined structure
where Corsair class "speculative traders" come from (and why it is a standard design )
how pirates can find a ready market for their booty.
Since this is accepted business practice for megacorporations, it stands to reason that planetary governments and rival nobles can use the same "rules" to justify their ethically challenged trading practices
The Imperial Government ENCOURAGES this kind of infighting, in order to keep the locals too busy with each other to seriously consider rising against the imperium.
If the Dukes are busing infighting they are less likely to band together to challenge the sector Duke or even the Emperor himself.
And no sub-sector Duke can have much authority over a megacorppration.