Here is a really simplistic explanation.
At pH = 14, based on Kw, [H+] = 10^-14 and [OH-] = 10^0 = 1
at pKa, [HA] and [A-] should be equal - but at pH 14, [OH-] is 1 M but [H2O] is ~54 M
So pKa is not 14.
What about 15.6? Here at pH 15.6, [H+] = 10^-15.6 and [OH-] = 10^1.6 = 39.8 M. Is [OH-] = [H2O]? If you take the molarity of pure H2O at 55.5M and divide by 2, [OH-] = [H2O] would be at 27.75M which would be a pH of 15.4
I think this difference between 15.6 and 15.4 has to do with the water activity at this extremely high [OH-]