We used to but stopped with the beginning of automatic aid. Auto aid requires a minimal staffing of 3. If your on your way back from an EMS run and catch a fire what do you do?
A dept that I used to run with housed 1 of each rescue,ladder and engine. For ems runs we almost always took the squad or utility to keep the big trucks available. In PA once I make patient contact I am not allowed to leave until care is transferred or the patient signs a refusal form. Several times a year we did have overlapping calls where the squad was on an ems run and we got knocked for a fire response. If we ran ems off the engine we would be out of luck for fire response. We did have more drivers for the big trucks than emt's for medical calls so it made sense to leave the big trucks. Add in the fact that it is much cheaper to run their squad (chevy tahoe) and it made sense at the time. Figure about 6mpg for the big truck vs 15 mpg or better for the squad, oil changes and other maint cost and its not a small amount of money you save. There were exceptions like daylight driver training, since we only had a handful of members that were able to answer daylight calls, the engine handled everything.
Just some back ground on the department: 300 fire calls, 500 ems calls annually with about 40 volunteers from 1 station covering about 15 square miles. The use 1- 100ft ladder, 1- 2000gpm engine, 1-heavy rescue (certified to PA DOH requirements for heavy rescue and QRS), 1- Squad (certified to PA DOH requirements for QRS), 1- brush truck, 1- utility pick up and 1-technical rescue trailer. Their equipment may have changed a bit since I left in 2009 but not much.