It's not a simple rerouting of a packet. It's a complete L5 decode/proxy/recode, inherently supporting only a few protocols. Putting this kind of functionality into the network is exactly what the end to end principle was reacting against.
(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.
2. You could make a similar argument about network gear having code to facilitate streams. Having a third party provide this functionality is further down the path of centralization.
3. Sure. The point is that to create/tweak protocols, you have to convince Cloudflare (etc) to implement.
It's the end to end principle for a reason. It's not a hard and fast rule, in fact there are many immediate reasons for wanting centralization. It's just unsustainable in the far term.