Answer:
My answer (that the information we have about codon structure is limited to the observations we can make now) is similar to the first part of your answer: that the number of amino acids that can be encoded is a function of codon length, in that both imply the (circular) argument that we must need more than 14 amino acids (plus a start and a stop, making 16) because we observe three nucleotide codons rather than two nucleotide codons. It would be nice to have a noncircular argumentf for why the minimum number of distinct amino acids is more than 14, but that is beyond my ability to construct
