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 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.