An elevator shaft or hoistway could make a swell chimney and double the peril by bearing what could be the most vulnerable folks in the house.
Much codified ado is made of fire-blocking wall and floor structure (and stairway structure to an extent), but not the eminently more airflow-permissive elevator shaft or for that matter the stairwell itself.
Laundry chute fire (and physical) safety will have to wait another time.
In regard to residential elevators and stairwells, what's at stake is fire-degraded wood stud walls and wood ceiling joists collapsing within hoistway or stairwell, engaging cab or stairway. Mid-landings in winders and longer runs, too.
As for residential elevator fire safety, this passage is from Before The Architect's House Construction Design Standards 1Q06 draft (edited from outline form):
