To the contrary, CDN pricing will usually beat cloud provider egress fees.
Common example: you can absolutely serve static content from an S3 bucket worldwide without using a CDN. It will usually scale OK under load. However, you're going to pay more for egress and give your customers a worse experience. Capacity isn't the problem you're engineering around.
For a site serving content at scale, a CDN is purpose-built to get content around the world efficiently. This is usually cheaper and faster than trying to do it yourself.