Why would you place such limitations on bandwidth? You can
transport a human body with a wagon. All cells and all information about them. It seems that the bandwidth to transport an entire human body is there and readily available, there's no physical limitation to stop it from happening. There's no specific reason why an energy beam of unspecified
kind wouldn't be able to convey the same information in a different manner.
Besides, nobody says that a transporter has to be beam-based, ephemeral microwormholes work just fine and are much less messy.