Favicons change very, very rarely, so they are perfect candidates for caching; fast extraction and caching are core features of Favicon Kit.
It was mainly the fact that Cloudflare does not cache by MIME type, but by file extension (https://support.cloudflare.com/hc/en-us/articles/200172516-W...) and/or would require page rules (https://support.cloudflare.com/hc/en-us/articles/11500320685...) to honor cache-control headers. (It‘s been a while since I’ve made that decision, so I hope I'm remembering the reasons correctly!)
KeyCDN was simple to set up and their pricing was equally simple and very reasonable, so I ended up staying with them.
I hope this answers your question, JohannesH!