We did extensive experimentation, and later user studies to find out that there are roughly three classes of people:
1) Those that use interface items with text 2) Those that use interface items with icons 3) Those that use interface items with both text and icons.
I forget details on the user research, but the mental model I walked away with this that these items increase "legibility" for people, and by leaving either off, you make that element harder to use.
If you want an interface that is truly usable, you should strive to use both wherever possible, and ideally when not, try to save in ways that reduce the mental load less (e.g. grouping interface by theme, and cutting elements from only some of the elements in that theme, to so that some of the extra "legibility" carries over from other elements in the group)
It's amazing that even in a space like this, of ostensibly highly analytical folks, people still get caught up arguing over things that can be settled immediately with just a little evidence.
https://www.youtube.com/watch?v=vetEg8J-wcw