WiFi, 5G, PCIe, Ethernet, QR codes, and pretty much any other classical communication protocol uses error correcting codes where classical bits need to be sent in blocks, e.g. for PCIe6, blocks of 256 physical bytes are sent, but only 242 of information is transmitted because the rest is used to enforce some classical correlation for the purposes of error correction. We can not send smaller packets of data (unless we pad). There are probably many technical details I am oblivious to here on the classical side of things, but this "can not split things up" constraint does not seem unique to quantum correlations (entanglement).
And the way we mathematically express and model classical correlations in classical error correcting codes is virtually the same as the way to model quantum correlations (entanglement) in quantum error correcting codes.
All of this with the usual disclaimer: the quantum case is much more difficult, engineeringly speaking.
What makes qbits valuable is that they scale superlinearly the more of them you have entangled together. This means 8 individual qbits can store less information than 8 entangled qbits. Since they have to remain entangled to do valuable work, you can't physically separate them to prevent interference the way you could with classical bits. This is actually really well demonstrated in all the protocols you mention. None of those protocols operates on a bus that can send 256 bytes of data all together at once. They all chunk the data and send a small number of symbols at a time.
For example in PCIe each lane can only cary one bit at a time in each direction. In typical consumer equipment, there are at most 16 lanes of PCIe (eg a graphics card socket) meaning there can only be at most 16 bits (2 bytes) on the wire at any given time, but the bits are sent at a very high frequency allowing for high transfer rates. This only works because taking those 256 bytes and sending them one by one (or 16 by 16) over the wire doesn't lose information.
I believe there are a couple of misconceptions in your first paragraph (but it is also plausible that both of us are talking past each other due to the lack of rigor in our posts). Either way, here is my attempt at what I believe is a correction:
- Both classical probabilistic bits and qubits need exponential amount of memory to write down their full state (e.g. stochastic vectors or kets). The exponential growth, on its own, is not enough to explain the conjectured additional computational power of qubits. This is discussed quite well in the Aaronson lecture notes.
- Entanglement does not have much to do with things being kept physically in contact (or proximity), just like correlation between classical bits has little to do with bits being kept in contact.
- Nothing stops you from sending/storing entangled bits one by one, completely separate from each other. If anything, the vast majority of interesting uses of entanglement very much depend on doing interesting things to spatially separate, uncoupled, disconnected, remote qubits. Sending 1000 qubits from point A to point B does not require a bus of width 1000, you can send each qubit completely separately from the rest, no matter whether they are entangled or not.
- Not even error correction requires you to work with "big" sets of qubits at the same time. In error correcting codes, the qubits are all entangled, but you still work with qubits one by one (e.g. see Shor's syndrome measurement protocol).
- I strongly believe your first sentence is too vague and/or wrong: "What makes qbits valuable is that they scale superlinearly the more of them you have entangled together". As I mentioned, the exponential growth of the "state descriptor" is there for the classical probabilistic computers, which are believed to be no more powerful than classical deterministic computers (see e.g. derandomization and expander graphs). Moreover, Holevo's theorem does basically say that you can not extract more than n bits of information from n qubits.
- Another quote: "Since they have to remain entangled to do valuable work, you can't physically separate them to prevent interference" -- yes, you can and very much do separate them in the vast majority of interesting applications of entanglement.
And the way we mathematically express and model classical correlations in classical error correcting codes is virtually the same as the way to model quantum correlations (entanglement) in quantum error correcting codes.
All of this with the usual disclaimer: the quantum case is much more difficult, engineeringly speaking.