It's as simple as the actual masses of atoms are very small and difficult to work with, that's all.
To expand...
I think logically, it would make sense to use the mass of the individual atoms as your result would be more precise or "true", but practically it would be extraordinarily hard to do.
Relative atomic masses are compared to the Carbon-12 isotope and averaged which is important. The values have been averaged and so in calculations the difference between using relative atomic mass and the actual masses of the atoms will be small. Relative atomic mass accounts for not knowing the mass all atoms as your relative atomic mass is the average mass of the isotopes in a naturally occurring sample of the element, taking into account the proportion of each isotope present.