The DC3 was very over built because back in those days aircraft designers didn't know how cheap they could go and still be safe. By the 1960s more was known about stress and fatigue in metals which enabled newer designs to be made lighter and to cost less while still meeting requirements.
Old airframes are often suitable for low utilisation specialised roles such as water bombing, oil slick dispersal, engine test platforms etc. The capital cost is very low, spares are usually still cheaply available, lots of down time is available for the increased maintenance and with low hours being flown, the higher fuel consumption isn't significant.
The January issue of "Airliner World" had a story about a B737-200 being operated in the freight role in the Philippines, it only operated between Cebu and the capital Manila with a round trip time of under three hours, most of the day was spent on the ground where maintenance was available and the basic analogue flight deck was perfectly up to the task.