Paraphrasing from the difinitive work on the subject "sector Fleet" by MJD
1. The job of the navy is war, that means it buys big ships to crush enemies.
2. Spreading your fleet out to cover everything at once is suicide. Fleets mst be concentrated ready to act anf fight as a fleet. You cannot afford to spend weeks sending couriers to find all your warships if someone invades.
3. Anti piracy is best done localy, system or subsector security who know the area and the peoples and who have light cheap ships.
It goes on with more points but these three cover the high lights.
It is NOT the job of the Imperial fleet to put down a dinky little pirate corsair. If said corsair pulls a raid while a naval ship is close then its some handy target practice for the fleet gunners but otherwise the fleet is looking out for subsector wide rebelions and alien invasions. The corridor sector has piracy, it also has the most powerfull naval fleet in the entire 3rdI. The fleet is there to deal with the doggy 30k cruisers not the 400dton corsairs though see above for target practice.
Every subsector of the 3rdI maintains a numbered fleet. These vary depending on the size, importance and wealth of the subsector. These subsector and colonial fleets are equipoed with smaller and older (read cheaper) ships and naval cast offs, this is where old cruisers and battleships go to spend thier last years of service.
The subsector fleets are more involved with anti piracy because the security of the subsector is thier main concern not the security of the entire 3rdI
Below these you have System forces, Hurscarles, Megacorp fleets (Al Morai route protectors, q-ships etc) and star mercs. These are all generaly under 1000dtons. It is these ships along with the subsector escorts that do the anti piracy work.
Now some of the problems.
The 3rdI is a mess, its full of backward worlds that cannot hope to produce even the most basic support for tech 12+ naval or ground units. The mains (jump 1 routes) on which the vast bulk of imperial ships travel use far too many of the backwaters to refuel.
There are a huge number of civilian ships out there. Millions of ships in fact. Some time ago I did some rough figures of how many hundred ships visit terra each day. The spinward main has tens of thousands of ships along its length and scores of systems with trillions of cubic Km to guard.
A small gas giant has an approx surface area of 62179600000km2. A standard ship with decent military sensors has a maximum detection range with minimal details (enough to detect an object as a ship) of 300,000km radius. How many ships are needed to be sure no pirate sneaks through and hides in the atmosphere of that gas giant.
There should be next to no piracy round the 100D jump ins of main worlds, major asteroid belts should be fairly secure due to the wealth of the mines so they will be defended. A main system gas giant will be defended against enemy attack, they will eat pirates for snacks,
However away from the main worlds pirates have a good chance.
If pirates are raiding traffic at some tech 6 backwater then modern ships need to be sent there, these ships need to bring in modern supplies. The transports that bring those (expensive and very piratable) goods then need to be escorted becasue there are pirates in the backwater systems.
Once you get ships there you can hunt down and wip out the stupid pirates and get the tri-d reportersround for a quote about your heroic victory. THe smart pirates have long since gone.
Piracy is a bit like a virus. While it is very small it can be un noticed, if it grows past a certain point it gets dealt with, hard.
Plus, what is a pirate. If they are only hitting ships of one world or one line then are they privateers in a legal war. Is it a personal argument, two companies having a dispute. Underhanded trade deals gone wrong. Local security after bribes and showing what happens when you don't pay the "system transit fee".
The 3rdI could be pirate free. It just needs to take away every private ship, nuke every world with a starport not under military control, ban every alien ship then shoot them on sight and acept that the economy just crashed. On the other hand if piracy is 0.000000001% of your economy and a handy excuse to have smaller warships visiting and snooping around all the time then so be it.
Sorry for the long post.