The OP said I should run my own infrastructure. I -could- host my blog by running a web server atop a server I administer, sure. I'd have to take on all the infrastructural tasks of doing that, securing it, ensuring any availability/scalability concerns I may have are taken care of, etc, but I -could- do that.
Instead, S3 + Cloudfront (or, sure, any flavor of hosting and edge caching options you care for; I was not implying "Just AWS") means I don't have to worry about any of that. For me, the reduced level of control, increased availability, scalability, and easy "it just works", is worth the tradeoff. As is the pennies per month it costs me given the low utilization and pay-as-you-go model. It's hardly a scam.