Having an AI tank a pirate raid usually ends in two ways:
1. The AI loses all of its planetary structures (and possibly the planet itself to bombing) and the surviving pirate ships return to the nearest base, bolstering their numbers at the base, or
2. The AI destroys every single pirate ship that was in the raid.

It looks like result 1 happened a lot for a few hundred ships to accumulate at the pirate base. As games go on, and pirate raids increase in severity, the proportion of Corsairs (the AI Heavy Cruiser) and Cutthroats increase. I would bet that the pirate base by then would be swarming with Corsairs, Cutthroats, a handful of Reapers (their flak) and the odd Rogue (light frigate) and Pillager (planet bomber).

Corsairs die easily to bombers, Cutthroats have the same armor type as LRFs, so fighters will tear those apart. Simply put, bring carriers and keep the pirate ships off of them with a well-rounded fleet (Subverters with Distortion Field make it easier by shutting down groups of pirates for some time).

Besides, 90 Enforcers?!? That's 1080 supply's worth. If you ran into an AI with bomber-laden carriers, your Enforcers would be converted to scrap fairly quickly.

With Vasari, I would recommend Bombers as Void did. Bring in a hefty group of enforcers to protect the carriers but the bombers should be able to handle most of the destroying. Also, bring in a few lower level caps for lots of free Xp. I'd recommend a Skirantra Carrier because it can field several bombers squads and has a repair cloud ability that can help keep your enforcers and carriers healthy. Also keep your fleet on attack local area only and make the pirates come to you, this way you dont have ships flying all over the place getting picked off, instead they'll be all together taking full advantage of you Cap ships and support cruisers (overseers and subverters) abilities, and be near the edge of the gravity well, making escape quick and easy should you need to retreat. Finally, keep at it, you'll eventually wear them down (and have lots of high level Cap ships if you keep bringing in new lower leveled ones).

well first off this is on the original sins not on entrenchment and ill give the ideas a shot.

Another option (for single player) is to use a pair TEC Novaliths and destroy the pirate bases from afar. Then the pirates will no longer spawn and you can just bypass them.

Nope, as of now the AI will never use a superweapon. And repeated Kosutra strikes could have really thined down the pirates for you as well, at least getting rid of the turrets for you.

That's something i never quite understood. Nonetheless, it is just one example of why almost no one plays an easy or medium AI unless they have less than a weeks experience (when i say that, I mean that you go to sleep at three in the morning after playing the game, and you start that playing session at about 7:30ish)