Is there an advantage or reason for them to feed in the opposite direction to jointers, router tables, and spindle sanders?
The structural reason is based on the orientation of the blade guides, specifically the thrust bearings. The blade's teeth cannot be facing the thrust bearings, or they would have no effect. Therefore, the blade is installed with the teeth facing away from the thrust bearings, and this determines the direction in which the material is fed (into the teeth, of course), which is left to right, because all band saws have the thrust bearings to the right of the guide bearings or guide blocks.
I can only guess at the reason for THIS (the placement of the guides, which ultimately determines feed direction), but I believe that it might have to do with the majority of users being right handed, making it a desirable orientation because the right hand (more dexterous hand) steers while the left hand pushes, and keeping the right hand farther out of harm's way - to one side of the blade rather than in front of the teeth.