Well, routing everything through them via DNS obviously means less code in your application, so that's nice.
Also, a CDN which routes all of your traffic via DNS can also take advantage of a private network to get the packets to your users faster, i.e. Cloudflare could potentially own a faster link between Virginia and Berlin than the public internet would take, and lower response time that way. I think that's what point two on the benefits list here is about: https://blog.cloudflare.com/cloudflare-is-now-a-google-cloud...