Yes, though it usually goes by other names. The direct version is site degeneracy classes - 0-fold degenerate sites are positions where every possible change is nonsynonymous, 4-fold are where none are. That partition is exactly the constraint you're describing, and it's already the denominator of every dN/dS calculation via Nei-Gojobori site counting.

For a per-codon "how bad could one mutation be" value, the usual construction is Grantham distance over the amino acids reachable by a single nucleotide change from that codon.

Why it isn't a standalone predictor: degeneracy is a property of the codon, not of the position. Every Met codon scores the same whether it's a catalytic residue or sitting in a disordered loop, so once you have conservation it adds almost nothing discriminative. It ends up as a feature inside CADD rather than a tool of its own.