Single sheathed boxcars (aka “outside braced”) are certainly not “all wood”. All wood boxcars were eliminated from interchange service prior to WW2. This was due to the inability of the wood underframes to withstand
the forces applied to them by heavier trains.
The next iteration would have been wooden superstructures with steel underframes. These also lost favor in the years prior to WW2 and were mostly eliminated from interchange service prior to the start of WW2. Refrigerator
cars often had completely wooden superstructures as well.
The next iteration would be cars with steel superstructure and steel underframes with wood sheathing, such as the single sheathed car that you mention. These began to be built prior to WW1 and lasted in service past
the time frame of this list. As for the MILW, they were likely not in interchange service at that time, but rather were in company service or MOW service.