Traditionally I think the deep trays were reserved for fixer, which could last a long time, but you did not wish to have saturated with silver too early, so you used lots of volume.
Fibre based papers once were exposed, developed, stop bath, first fixer, water holding bath.
At the end of a session, from the water holding bath all of the prints together were moved into a fresh second fixer solution, and interleaved to make sure all prints saw exposure to the fresh solution.
These were where having a deeper tray was handy.