if it means destroying the very essence of that character's personality, am not sure if it's worth it to save time and money.

That's a matter of opinion, and I disagree personally.

you are right on that count..we don't know. But what we do know is that it would be probably the very last option he considers. but in the show all that happened was "Ramsay's 20 good men attack" and some snowy blizzard and apparently the greatest military tactician who has suffered worse military odds was desperate enough to burn his own daughter who he prophesied to love and care about 2 episodes ago.

Well to be fair, he says no burnings no matter what and then like a chapter later is burning people, cannibals yes but he still changed his mind like that. And he's shown to at least think about burning a child relative in significantly less harsh circumstances before in the book. I think there are more than enough quotes to back up the possibility that he might burn Shireen, I agree in the books it will likely be in a worse position but it is definitely possible. Here's where the constraints of the show come in, him burning Shireen is a major, major plot point that they have to include, but the situation he's in when he does that in the books may be something they can't do for one reason or another in the show, so they had to create some reason for him to do it. Whether or not he should have let his supplies get burnt (I've argued this to the death and don't want to get into it again, but it's at the very least debatable and not a sure thing that this was unrealistic), the situation is he has been convinced Mel's magic works, and he has to either let everyone die including him and his daughter by starving and freezing to death, or kill his daughter and rely on Mel's magic. Stannis' pragmatism and quote about "One life against a kingdom" make this entirely realistic to me. It would have been boring beyond belief and they would have gotten endless shit for showing the camp starving and freezing any more than they did. Condensing thousands of pages into 10 hours is going to mean some hard decisions and some parts of the show that pale in comparison to their book counterparts.

Maybe they went in a different direction than a lot of people would have liked, but I posit that they had to with some storylines and it just so happens Stannis was one of those whose had to take a hit. Your response was reasoned well and was polite, but any comments on character assassination or butchering are asinine gibberish.