Even the Soviets and other organized military forces that employed women out of necessity have generally known better than to deploy them in mixed units with men. That's opening the door to a lot more trouble.
If by "meme" you mean her influence was made up after the fact, that's not true. Plenty of contemporary sources on both sides of the conflict didn't take her lightly. But again, this wasn't because she was running around chopping off the heads of Englishmen. It was because of the effect she had on the French soldiers' morale, and that was because of both her skill as a public speaker (a very religious themed one), and her complete confidence in French victory (which may have been because she was touched in the head). Basically, because this 90 pound girl was so absolutely confident and fearless, the French soldiers were inspired to be too, when they'd previously been at their lowest point. Morale matters, and it mattered even more back then. A lot of times the winner of a conflict was simply the side that chose to keep fighting instead of running. The psychology of war is no less real than the physical side of it, and in that regard figurehead leaders like Joan of Arc matter.
As for being given the choice to go to prison or be burned, that never happened. After being captured by the Burgundians, she was moved between several prisons of both the Burgundians and the English and tried to escape multiple times, before the English put her on trial for heresy. The plan of the trial was always to kill her. She was already in prison, so why would they even bother with an elaborate trial just to ask her if she wanted to be executed or go back to prison?