Are there any building code considerations (e.g., chimney effect for a fire) regarding a multi-floor wiring chase? Isn't this why laundry chutes are no longer permitted in some places?
Riser or plenum rated cables are required by code if you go between floors, except in plenum rated conduit. Conduit is usually more expensive though.
Non rated cable more easily catches fire and makes a lot of smoke. Plenum rated cable is about twice the price, but ethernet is pretty cheap for a single home.
I've also been curious about this in the context of making a dumbwaiter, but not enough to do the research. I would think having passive automatically closing fire rated doors would take care of it, but I don't know.
You could look into it but I think the reason laundry chutes aren't made anymore has more to do with kids getting stuck in them and less to do with fire code (after all, stairways are chutes connecting floors).
Of course there was another solution (I’m assuming you’re not still in the chute, by the way) - which is to make them so big that even a large adult male can’t get stuck.
But the main reason they’re gone now is that people put the laundry on the same floor as the bedrooms in modern homes.