Yes, It will be better to make hydrogen as standard of atomic unit. In this way, we can easily relate the masses of isotopes, mass defect, binding energy and masses of sub-atomic particles.

Hydrogen mass is due to its proton; Carbon 12 has six protons and six neutrons, and so its mass depends upon both types of nucleons.

Carbon-12 is common, stable, and provides a uniform standard for mass, hence is probably the best choice for the amu.