Thanks to all for the help & comments. I've played a few more games out and I think the main thing about the pirates that bugs me is the inconsistent difficulty. Playing random maps, depending on how the map is set up, you can put up a chokepoint or two for the pirates, or they might be able to get at different planets from different directions. Early on, splitting fleets only makes the pirates harder to fend off, and putting up a pirate-stopping defense in two or three places is too costly. They still hit hard initially and I guess that's what was throwing me off, especially when the map didn't offer an easy chokepoint. The later game is definitely much improved. Once your economy is going, fending off pirates is straightforward as long as you're paying attention and not skimping on defenses.
I did have one odd game where the pirate raiding fleet got a little bit stronger each the first couple raids, but then went up and down. My fleet and the computers' fleet were slowly growing the whole time, and we were both expanding.
The fleet sizes were:
10 Cutthroats, 5 Corsairs, 11 Rogues (handled by a repair bay, a few defense platforms and a small fleet)
10 Cutthroats, 8 Corsairs, 12 Rogues, 6 Reapers (wiped out an AI asteroid)
10 Cutthroats, 4 Corsairs, 12 Rogues, 2 Reapers (came for me, and I had a bigger fleet than the AI at this point)
10 Cutthroats, 8 Corsairs, 12 Rogues, 6 Reapers (came for me and gave me some difficulty)
10 Cutthroats, 5 Corsairs, 10 Rogues, 1 Reaper (came for me)
So I guess there's some random factor, but the raiding fleet power seems quite variable.