And you have to like all of them, so you need at least 10 to choose the 6 from.
occasionally, you might actually need/want all 10.
In what situation?
some kind of electronic function test.
something with many sensors.
troubleshooting/analyzing a multiple channel power supply
there's a bunch of RF applications
characterizing a whole system for repeatability
the 3458a feels like the defacto physics research bench DMM. to save money, many labs combine it with a switch system to have multichannel capabilities. which gives you similar capabilities to multiple DMMs: I've seen this more often in SS&CM physics. on the other hand, I've also seen some labs equipped with half racks of 3458's and a high speed switch system for faster acquisition and higher accuracy or to ensure certain sets of measurements are done simultaneously: more common for particle physics.
addendum: need for 4 -> it's pretty common to want 2 voltage readings and 2 current readings simultaneously.