IanW said:
Dlpulver,
Assuming you are the legitimate authorities and can make as much noise as you like, if you try really, really hard, you can make the space out to 100 Diameters vulnerable to pirates.
There also the problem that "If the world is one that does not have extensive interplanetary trade (probably limited to starport C+, pop 8+, TL 9+ worlds, or asteroid belt-only systems) they can make that calculation." its also not going to have enough trade to keep a pirate in business
I agree the cost of protecting against piracy is relatively cheap and all of your reasons are logical. All comments below apply only to my own universe; piracy is an issue that one can never win an argument on, as it depends on so many other assumptions in and out of canon.
IMTU, not every government or bureaucrat is wise, and the longer that piracy is successfully suppressed, the more likely it is that even a minimal space defense budget will be cut to near-zero either to deal with an on-planet threat or some other governmental expense, or, more likely, left a hollow shell that exists more on paper then in reality. Same's true of the sector and imperial navy: even if patrol ships are only 1% of the budget, if a subsector hasn't seen pirates in 50 years, some pencil pusher is going to recommend the credits that supported that deployment be diverted elsewhere, or patrols cut back. There's always something else that needs money and resources, and any large organization has a thousand different people demanding it, some of them with power. It's sort of like the way minesweeping is ignored my some wet navies today - it's a key area, but it hasn't been a huge threat. (Or the way New Zealand have decided that fighter and strike aircraft aren't relevant to their situation; instead they've got a navy/air force that is good against pirates and the like...
IMTU, a lot of worlds in the Imperium are more likely to be in the reverse situation: the Imperium protects them, in theory, against external navy threats and they pay taxes to it for this reason. Instead their big focus is internal security: dissidents, rebels, etc. So all their limited miltary money goes to ground and COACC forces, or cops, or social welfare, or whatever. And while they're supposed to fund a minimal navy, often this atrophies because if no one's seen pirates for a long time, why worry about them? And then, once in a blue moon, some pirates do appear.. but the disruption they cause by taking a 200-ton merchant ship and moving on is actually a lot cheaper than the few MCR a year it takes to fund even a minimal space force.
Also, some of the ability to deal with pirates depends on assumptions. For instance, near as I can tell, in MGT there's no way to detect a target beyond about 25 planetary diameters: sensor range even with extended arrays seems to max out at about 300,000 km. (This was also the case in CT, though not in several other versions - the whole "no stealth in space" discussion seems to have originated with T4-era debates). This imposes issues both for the pirates themselves (finding targets, though perhaps mitigated if they home on transponders) and for planetary defenses. How missiles work and their maximum range is another tricky issue that has varied from edition to edition; in MGT they seem relatively short ranged.
Much of it depends on how much piracy is happening. A single desperate captain doesn't need to worry about whether a backwater system can support pirates - he may jump into three or four backwater systems, maybe diverting to gas giants to refuel or pretending to be a trader if there's no targets, before stumbling on a free trader or type R in the right location and the right moment. Maybe an ideal target system is one that gets an average of one 200-ton ship every 2-4 days or so, maybe 10,000 d-tons of cargo going through it a year. Enough for fair odds of meeting something; not necessarily vital to the economy.
Anyway, that's how it works in my game; your own mileage can vary!