(1) Cloudflare does do BGP-based protection (rerouting of a packet) on their enterprise tier.

(2) They really aren't adding functionality into the network. If I put a cluster of Nginx servers in front of my web server, or if I have Cloudflare do it for me, I don't see how that fundamentally changes anything.

(3) The Cloudflare approach of an application layer proxy is feasible for any protocol which can be proxied. I've worked on SMTP proxies which do to SMTP what Cloudflare does to HTTP. Cloudflare also has a DNS proxy. Proxying is a perfectly valid and often incredibly useful technique.