So if the insides of the drawers have a poly finish, then the outside
should also.
....
Since normally a chest of drawers has the drawers closed, you won't get
a lot of air movement over the unfinished surfaces, so the amount of
imbalance is much less than the bottom of a table top. *(And even there
I've seen unfinished bottoms.)

Yep, had the same thought and was just speaking theory. For my own
work I take the extra time to finish all sides just for consistency
and a finer finish. I love wood but bare wood is closer to lumber than
furniture in my estimation and can stain, pickup body oils, and be
prone to problems if some water based accident occurs.