Forget the unscientific subjective morphological classification.
Morphology is still important in making observations about living organisms and their interrelatedness. It is an essential starting point, but it is no longer the last word.
We created the table of elements without seeing any elements.
Um, what? Are you suggesting that iron was invisible before 1869? What on Earth are you talking about?
We should be able to do the same with DNA.
Why? The periodic table was predictive because it arranged elements by the their atomic number, leaving gaps for the then-unknown elements. DNA just doesn't possess the same properties.
The chemical elements are the simplest units in chemistry. The simplest units of information in DNA are the four bases, A and T, C and G. Are you suggesting that we arrange these in some order that will predict the "missing" bases? I hope not, but I can't otherwise imagine what comparison could be made here.
Mutate and Survive