Actually, I encountered pretty much your situation yesterday, a large group of Kusari were in Dublin, with little chance to repel them by myself, so I logged a battleship with 5 solaris, I didn't run in guns blazing and RP'd the situation as realistically as possible 'stationary trade protection' and all that jibber jabber, thereafter BMM started calling me incompetent. I waited until they started attacking Miners and simply tailed them, I got into range of the miners and they simply ran away, I did this until they left the system.
What I suppose, is that the military are there to keep peace in the most dangerous parts of house space, Dublin, Califorina/New York, Kyushu and whatever Rheinland has for pirate active systems. The Battleship Essex is in Dublin to prevent damage to mining industry, Battleship Nagumo is at the Kyushu gate to prevent smuggling/raids from tau 23, non-vanila Bs outside planet Stuttgart to protect the interests of the planet and so forth. Most stationary Battleships are used to protect economic interests.
To sum up, Military are to keep peace in 'flashpoints' and police are there to stop smuggling and low intensity crime/piracy, every other security orginsation is there to do the escorting of traders no matter how much they demand that you escort them, they need to hire people. Use of heavies should only be used to hold choke points and not really to chase people and barge into fighter vs fighter pvp.
There, a capwhores Raison de etre on a plate for any wannabee capwhore, send your thank you letters in the post.