Agreed! Current implementations (even this one I suppose, althought I didn't have the time to check) use either websocket or older hacks like client-polling or Flash sockets. Time to enter to the future! :)
There already have been a few nice VNC web clients around for a few years, like NoVNC (http://kanaka.github.io/noVNC/, python server-side, used in Openstack and others). Unfortunately, there's no magic: you need your VNC/RDP server, then your "clientless server" (proxy socket<->websocket or alike), then your web server to host the "clientless" client.
It's becoming to be interesting when your VNC/RDP client directly supports websocket, eliminating the need of a proxy and only use a STATIC web server to host client. Wait, it's built-in for qemu since 1.4! http://git.qemu.org/?p=qemu.git;a=commit;h=0057a0d59006d00c2...