This is SO out of Character for Stannis, just for Shock Value and giving the Audience a Reason to Root Against him.
(CONJECTURE! but not like that matters much anymore with the direction they are going)
But I am starting to think that they had Stannis do that so we can justify Brienne of Tarth Killing Him when she goes to Rescue Sansa, her getting distracted by her revenge "fur da Renlys" and much Like a Parallel they are doing with Ayra being distracted with her Mission.
A plausible conjecture, for sure. I believe that Stannis meets his end in TWOW, and your theory works well to satisfy that end, and it just consolidates some storylines.
Stannis is the ultimate sufferer of “middle child syndrome”, and his quest for the Iron Throne has caused him to spiral downward in a very bad way.