Alternative definition of the mole? 1 amu (atomic mass unit) is defined as the one twelfth of the mass of a carbon-12 atom. The mole is defined as the number of carbon-12 atom in 12 g of carbon-12. In other words, 

$$\require{cancel} 1 \textbf{ mole} = \dfrac{12 \textbf{ g}}{m(^{12}C)} = \dfrac{\cancel{12} \textbf{ g}}{\cancel{12} \textbf{ amu}} = \dfrac{\textbf{ g}}{\textbf{ amu}} $$

I believe that the 12 g were chosen so that the mole could exacly express the ratio between the g and amu. 

Consider now this alternative definition : the amu is defined as the exact mass of a proton and the mole is exact ratio between the g and the amu. Wouldn't it be simpler this way?

What are the advantages of one definition over the other? Is there any reason we would want to keep the former? Why scientists decided to define the mole like that and not pick a simpler definition like the one I proposed?
One of the reasons to take Carbon-12 could be that it's hard to get your hands on one mole of pure hydrogen (and to weigh it). Carbon-12 is a (room temperature) solid which is relatively easy to produce, keep pure, store and weigh.