What would you have him do?
Say, "Hey, you know, if fate requires me to burn my only daughter at the stake in order to not freeze to death in the snow with my army and go down in history as a failed would-be-king, I think I'll just freeze. It's just not worth it. There are some things a man simply must not do."
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Looking to the structure of the episode, I'd say the Danaerys storyline, which picks up directly after Shireen's death, is a subtle commentary on the likely outcome of Stannis's decision.
Like Stannis, Dany was put in a tough position, where she had to go against her principles in order to save herself from a quagmire of her own making. She caved on the fighting pits, and what did it get her? This close to getting murdered by a mob of dudes in creepy bronze masks.
The dragon's fire, burning the masked attackers alive, was obviously supposed to make you think of Shireen. Dany's salvation also comes in the form of a beast that burns people alive. Unlike Mr. Baratheon's savior, Dany's is able to fly her away to safety. But at what cost? All of her closest allies are left behind in the stadium with plenty of attackers still alive, and it's not like any of the problems in Mereen have been solved.