From observing other games, this is what causes rubber-banding, I would assume. When you lose connection, the server doesn't track your movement then resets you to where you were when you lost connection. Wouldn't you teleport on the server if the player had authority? Couldn't you also hack noclip by setting your location with an external program?
I understand that you want to have the client move instantly, but this seems to come with some vulnerabilities.
I'm not sure what part you're referring to. When movement is not properly synced, yes you can teleport. That's just common with network games. It does it's best to keep track of movement across the network, but if it missing a few steps along the way it'll just update to where the actual new position is and move you there. There's always ways to hack a network game, even AAA games have problems with hacking.