Sorry to take so long to reply, Joseph, but it's not always easy to explain this stuff.
I'm not saying that the 16 bar form is not valid or not useful, I'm just saying the 12 Bar form is simpler, and easier to use.
Rather than talking about the blues as simply 12 measures, it's more useful to break it into three four-measure phrases.
Next, you break the four-measure phrase into two measures (eight counts) of exposition and two measures (eight counts) of recapitulation.
The blues moves through three chord shifts, the Tonic, subdominant, an the dominant. The 12-bar blues allows a a two-measure exposition and two-measure recapitulation for each of the three chords and we're done.
It's important to note that in each four-measure phrase the exposition is restated in the tonic, subdominant and dominant modalities, but the recapitulation is always on the tonic chord.
With the 16 bar blues, it's necessary to modulate to the sub-dominant a second time, which, because there are three chord shifts, but four four-measure phrases, means there is extra emphasis on the sub-dominant.
Again, it's not that you can't do it, it just creates a more complex structure, and one that it a bit out of balance.