Do you think Starfleet gave some of their ships to allied Federation members? Could there be a Galaxy Class starship out there with Andorian personnel?
I assume there would. I mean some species would be taller and larger and find the seats, doorways and control panels a little smaller and lower than what is comfortable. A very short species would find the seats too large and difficult to reach all the panels and controls at their station or on the walls. Their ships, even if Starfleet, might have different seats in the work areas and different seats and beds in their quarters, with all the control interfaces on every deck at different heights and shapes to accommodate them.
Remember Worfs standing station on the ENT-D? How would a species averaging 3 or 4ft tall operate that? And one averaging 8ft tall would find it too low. Even the seated stations require you to reach in order to operate some controls. That would be a little too far to reach with very short arms. Just picture 10 people from a Yoda-sized species sitting at all the stations on the bridge. See a problem?
That's aside from the slight differences in atmosphere, temperature and gravity that each species evolved in and would prefer to work in. The more you think about it, the more unlikely it seems that every species could really serve equally on every ship together.
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