IIRC, Yes
Laundry chutes are against many local commercial and residential new fire codes.
When one worked in hospitals, many of the older ones had laundry chutes for sending soiled linen down to the laundry, or an area where it would be collected, not sure how many new hospitals are but with them today if any.
Basically as the other poster stated, laundry chutes can act a a chimney and send any fire right through a building.
At least in hospital/commercial settings, there was also the point of keeping "germs", dust and what not from soiled linen being dispersed up and out the chute each time items are sent down. Some old hospital design books dealth with this by various suggestions for construction and or methods for keeping the chute clean.
Same applies to rubbish chutes found in many older apartment buildings that once emptied into an incerator or rubbish heap. Ideally they should be steam cleaned once a year, but that rarely happens. They are however an excellent vector for the bad odors, fumes and germ laden air from the rubbish below to rise up and pervade a building. In some parts of the city where the building is lax about emptying the compactor or otherwise taking out the rubbish from the bottom of the chute (indoor incerators long since banned), tales of vermin "climbing" their way up is not uncommon.
The last bit can make for a rather interesting surprise to anyone opening the chute door! *LOL*
Didn't the Brady household have a laundry chute?