As most you know the measurement of atomic masses has > 200 year old history and atomic masses were deduced on the basis of chemical reactions by meticulous chemists until the 1940s. Later, mass spectrometer became the tool for determining atomic masses. In each case, scientists assigned one of the elements an arbitrary number and calculated the masses relative to that. For example, early chemists like Dalton, set H as exactly 1. Later, O-16 was set to 16 exactly. By the 1960s, C-12 was chosen as the reference and its atomic mass set to 12. Today, all atomic masses in the periodic table are relative atomic masses with C-12 as a reference.
What puzzles me is that if all atomic masses are relative to one particular element, what is the actual mass of an element? All these definitions were chosen by chemists without any theoretical justification in the past. I mean O-16 was set to 16 when the concept of atomic structure was not even clear.
With the experimental availability of Kibble balances and perfect silicon spheres, would it be possible to get rid of relative atomic masses in future and find the true (absolute) atomic masses of elements?
P.S. Edit The mass of carbon or oxygen atoms originates from a circular definition (as posted in the answer). All these masses are calculated on the basis of assuming that 1 mole of C-12 atoms weighs 12 g exactly. There is a long long history behind it. I didn't want to repeat all here. I am not worried about kg or anything else. All I am saying is that would new approaches like the Kibble balance allow us to get rid of relative atomic masses?