You are absolutely right. And when a corporation is damaged in this manner, it has the opportunity to show its actual damages for staffing, promotions, contracts, and everything else.

The issue with statutory damages is that they are awarded without regard to actual injury. They act, more or less, as a punishment or deterrent. So even if the corporation truly suffered no damages, it still can receive a few thousand dollars. (Note that taking statutory damages is an option: if your actual damages are higher, you can opt for those instead.)

I'm not necessarily saying that statutory damages are a bad thing. The problem I see is the inequality in their distribution: because copyright registration is costly, statutory damages are ultimately only available to the profit-seekers. One possible idea would be to cut out the registration fee, making it easy for everyone to register their works and thereby receive equal protections.