What people believe that is not true.
THAT IT MAKES ANY SITE FAST
It caches static assets. Pages still reach your server unless you configure otherwise.
A slow application remains slow.
THAT IT REPLACES SERVER-SIDE CACHING
It does not. Server-side caching addresses page generation, which is where most slowness lives.
THAT IT PROTECTS AGAINST HACKING
It filters traffic. It does not patch your software, and a vulnerable plugin remains vulnerable.
THAT THE FREE PLAN IS CRIPPLED
For most small business sites it is entirely sufficient.
THAT ENABLING IT IS RISK FREE
Mail breaks if records are proxied. Redirect loops occur if SSL mode is wrong. Functionality breaks if Rocket Loader is on.
THAT IT HIDES YOUR SERVER COMPLETELY
On shared hosting the address is discoverable, and mail hostnames reveal it necessarily.
THAT DNS CHANGES IN CPANEL STILL WORK
They do not, once Cloudflare's nameservers are in use.
THAT IT BACKS UP YOUR SITE
It does not. Always Online serves a cached snapshot and is not a backup.