They do routing. Even if you're connecting to a non Cloudflare server, the traffic may still be routed through their servers.
Why would they want to peek traffic? Most likely for statistics (most frequently visited websites etc).
Can you give an example of a BGP route or traceroute to a site not on Clownflare that was routed through Clownflare?
Can you give an example of a BGP route or traceroute to a site not on Clownflare that was routed through Clownflare?