Did unfinished attics serve a functional purpose in old houses?
Not functional, but cost. Roofs have slopes to drain water and slough snow. It's the nature of their design that there's a hollow below. Since the finished space is relatively small, and since it costs more to build a floor robust enough to carry  people and furniture, and since it costs more to finish the space and insulate and add (larger) windows, and since the space was useful as storage without being finished, and since people back then were happy with less space and fewer things, they didn't bother. 

An indirect benefit to an attic, as opposed to a completely open roof cavity, was that it didn't need to be heated. Lower ceilings keep heat down where the human inhabitants are. 

Obviously there's some energy efficiency to be gained by having enclosed attics above a ceiling in an uninsulated home, but that's not the primary reason attics were built. Drainage (and to a lesser extent, style) were the main drivers.