AWS doesn't give you console access, does it? Or at least I haven't been able to find it. I know on Linode they have LISH (console over SSH) and Xen will give you a VNC console (I think Vultr and Digital Ocean can too).
It seems like a much more useful feature is simply being able to see the console on the VM itself. Often kernel panics will print information on the default virtual terminal.
FWIW, GCE have console. Another thing I miss in AWS is the ability to change instance user-data while running (GCE also allows this, including the ability to long-poll for changes)
Rackspace (at least, when I worked for a company that used them) has access to the console; their website has a link to a VNC page (running a Java applet) that connects to the console of the VM; you can even type into it, unlike AWS.
It was extremely handy, and I miss having it. Debugging issues in AWS is a bit trickier.
It seems like a much more useful feature is simply being able to see the console on the VM itself. Often kernel panics will print information on the default virtual terminal.