Depending how many bits there are in the bitmap, this isn't true until you pass a certain number of pieces of gear stored thusly. The bitmap takes up space all the time, whether it's in use or not. So, you're suggestion of a bitmap means that if one piece of gear is stored for a single character, all the space is used, regardless of whether you have any other items or not. While it's probably safe to assume the number is not huge, the impact of the bitmap on storage space could easily be in the range of 20-40 pieces of gear before it becomes relevant.
If you consider how many people would store one or two pieces of gear this way, and nothing more, the total system impact of the bitmap method is quite high and actually adds to the storage space problem.
