As a number, well nothing. I'm not saying there are anything wrong with the numbers, I'm saying that with a standard set of imperial or metric tools, you're more likely to find your imperial tools working with with you.
> And what's going to happen when you divide by three, not two?
Well dividing by three will be 1/4". That's another common imperial size. But to answer the point I think you were trying to make, there are sometimes cases where it isn't natural — like dividing 3/4 by 5. In those cases you need to measure or pull out of divider. Your problems don't all disappear when using imperial but I find that more often the perfect dimension happens to be that of a commonly size tool.
> Don't see anything natural in one compared to the other.
I think you're arguing from the perspective of pure numbers verses the practicality of making something with tools that I own. If I was using CAD, it metric or imperial would make zero difference.