It's a good question, but:

> might be tricky to distinguish chemically during the protein synthesis process

No, amino acids are bind to tRNA by special proteins that have handiness and can easily distinguish the L and R version. Most proteins can only operate on one handiness of the target molecule.

> making e.g. different codons for left and right-handed amino acids infeasible to implement

No, there are 64 codons and we are using them to map only 20 amino acids and a stop signal. So there is a lot of duplication. Some bacterias have one or two more amino acids or a small tweak in one or two of the conversion table, so it's possible to add more stuff there if necessary.

My guess is that mixing L and R amino acid would break ribosomes. The ribosomes read the mRNA and pick the correct tRNA and connect the amino acid that the tRNA has. I guess that the part that makes the connection assumes the correct handiness of the amino acids.

Going down the rabbit hole I found https://en.wikipedia.org/wiki/Nonribosomal_peptide that explains that some peptides (that are like small proteins) are formed by special enzymes instead of ribosomes, and some of them have D-amino acids or other weirs stuff.

> No, amino acids are bind to tRNA by special proteins that have handiness and can easily distinguish the L and R version. Most proteins can only operate on one handiness of the target molecule.

Ah, neat. That was the step where I worried about coding being infeasible, too, coding for R amino acids wouldn't do any good if you couldn't distinguish them. I did know there was plenty of room in the encoding scheme.