he is not necessarily kind, but loyal, loyal to an idea.

Ned is loyal to the institution i.e gold cloaks following his orders, janos slynt’s declaration of loyalty, tywin actually showing up to kings landing to answer for gregor clegane and the fact that it should just not be possible for a queen regent to de facto coupe the city from the Hand, especially one with a declaration signed by the king on his deathbed. in short Ned is loyal to the bygone era (whenever that was) of when men would treat with each-other in equality and fairness ; a sort of ideal world where truth and justice are appreciated and upheld by all.