Hm, reading that it is not immediately obvious whether you mean (c+d)/3 or c + (d)/3. At that point I think it should be straightforward to implement {}/{} as syntactic sugar for \frac{}{}.

Mathematics notation is basically completely determined by consensus and people come up with new notation all the time whenever they need it. In particular, in order to convince someone that your notation is better you have to show previously how hard stuff becomes easy and not how easy stuff becomes even easier.