Like a lot of things that seem odd today, the f stop is a historical tradition.
Early photographers, were manually setting their camera exposure, and in the very early days without the help of a light meter.
They needed a way of expressing the light passing capacity of a lens in a way that was portable (you didn't need to learn a new set of numbers for each lens), easy to remember/use (didn't want to have to do math every time they took a picture) and proportional to shutter speeds (so that you could easily trade off aperture for exposure time). The scheme that was ultimately adopted was what we know as the f stop.
So these f stops weren't metadata, they were (and for some cameras, still are today) part of the physical controls on the lens barrel used to control how much light struck the negative.
For a more complete overview of the history, see wikipedia:
http://en.wikipedia.org/wiki/F-number#Origins_of_relative_aperture
Looking at the article, it also seems that there is a difference between the effective aperture and the size of the physical aperture. This would be another reason to use a dimensionless ratio instead of a physical size.