Yeah, I think that would help.
It also feels related to: Custom sidebar sections being tested on meta - #29 by simon_tomes
There’s something about the consistency of offering the same UI icon/button/link in different contexts that I think is helpful. As in, if people in one context recognise that < equals see all the chat channels then they might associate < with see all the chat channels regardless of context e.g. in minimised or maximised mode.