why do academics write peer reviews?
I think academics are paid to perform peer review, in the same sense that they are paid to do research.  I don't have a boss telling me what to research and paying me when it's complete; rather, my university expects me to perform research that is judged significant by my peers.  In the same way, my university expects me to perform peer review.  In my annual reports to the university, I report my research outputs and I report the journals for which I have performed peer review.
You may argue that my continued employment and promotion depends more heavily on my research than on peer reviewing, but the same could be said when comparing any of my service or teaching duties.
The bottom line is, academia is a gift economy, and if you want to be part of the community, you're expected to do peer review.