Here is my thinking about why they did not finish dresser and chest drawers way back when.
Unfinished drawers will absorb moisture and release it again according to the local environment. Local environment being the bedroom. So as the room got damp, the wood would absorb the moisture, probably from the clothes also, and then when it was drier, the drawer would release the moisture. There wouldn't have been much moisture that we are talking about so the drawer was more or less breathing. If there was no breathing, like in the case of a hard finish, the moisture would collect in corners and mildew will form. So they were preventing mildew. This is more noticeable in boats with interior living space. I winter when the boat is at it's dampest, the moisture will collect on hard surfaces, whether it be finished wood, plastic laminate or fiberglass. This would result in mildew. The unfinished drawers have no mildew..
As I said earlier, I have not read or heard of this anywhere, just my conclusion based on my experiences.