I guess it depends how centralised your tube network is, but I can't see how it would be economical at scale. For a intra-building sized deployment, sure, but metropolitan tube-to-the-premises network with hundreds or thousands of endpoints per node you'd surely need automation.

Plus, it would be pretty simple to adapt internet routing architecture to the tube sorting machines. As long as you can embed a destination (node and endpoint) address in a barcode or NFC tag on tube ingress to act as your "packet header" you can leave the routing decisions to the tube sorting machines much like existing interior gateway protocols.