I don’t understand why they couldn’t do that either. Above my paygrade, V, sorry!
Eliminates inspection, stateful or otherwise.
Just thinking out loud ....
Probably, simply because it doesn't change anything, if the source or transmission is tapped / monitored in-line (i.e., non-quantum transport):
It's already being done. It doesn't eliminate or has anything to do with inspection (I assume "stateful or otherwise" refers to the firewall/IDS/IPS, which has nothing to do with the data transmission, as they operate on higher OSI layers).
Data has to be re-assembled at the end point / receiver. If the header is symmetrical (i.e., the data directly follows the header) splitting the packet doesn't do anything to prevent decoding.
If the header is asymmetrical, the header must contain the pointer to the data packet in order to be reassembled... again, nothing there to prevent decoding, except the usual PGP / RSA key exchange mechanism.
Quantum technology simply adds the step of preventing the tapping of any packet exchange; it's another (and more rigorous) layer of security at the OSI physical/PHY Layer 1 (which is generally not specific to the TCP/IP protocol), below the DLL/Data-Link Layer 2.
More technical explanation: Optical Networking for Quantum Key Distribution and Quantum Communications (1.1MB PDF file)