Small departments might want each station's first-out vehicle totally independent of the rest of the fleet. Some call that a common standard of care. Contrast a first-in unit that can do it all with many departments' specialty apparatus, which have their own problems. Many departments have specialized rigs to the point that they are all single-purpose apparatus. You'll see tankers that can't self-fill.
Crews have to decide before every call which fire truck to take.
First-in units might not carry enough hose to reach the closest hydrant. Crews drive apparatus without floodlights and generators. On the fireground, a crew might notice that the needed ground-ladder is still back at the station. If the foam rig doesn't arrive, the attack has to wait. Lots of engines have to rely on a tanker that might not respond to support them on the initial attack.