The reasons I have read for oil applications include adding weight to the plane (I tend to disregard that as significant), and to prevent humidity from affecting the wood. I have also read that professional conservators say that BLO will degrade the wood over long periods of time and promote the use of quality paste waxes.
Considering that my planes are users and not true collectables, I prefer to clean them, apply a little BLO just for appearance purposes and then apply a quality paste wax just to help keep humidity issues down. If you rework any of the planes so that you expose bare wood you should apply something for the reasons above and to help keep the surfaces cleaner. It has become trendy to use animal fats on the rubbing surfaces of the planes but I understand that it blackens wood over time. I just use paraffin to reduce friction. since it needs to be reapplied periodically during the work.