I don't find Dany's execution of nobles who refuse to submit to her particularly problematic from a medieval history perspective. Yes, it was typical for nobility to be ransomed rather than killed in
most battles of the high-medieval period and on, but certainly not all; and civil wars often inverted the rules. Specifically, much of GoT is modeled on the Wars of the Roses, in which we know,
according to Philippe de Commines:
King Edward told me in all the battles which he had won, as soon as he had gained victory, he mounted his horse and shouted to his men that they must spare the common soldiers and kill the lords, of whom none or few escaped.
This is, notably, even less merciful than how Dany is acting. Now, how often Edward actually carried out this verbal threat in full is contested by historians, but it certainly was at some points --
after Towton, for example:
Thomas Courtenay, Earl of Devon, the son of the Earl who had originally backed Edward's father and had then forsaken him, was taken prisoner and beheaded in York a few days after the battle. James Butler, Earl of Wiltshire, suffered a similar fate when he was captured a few weeks later. According to Gregory, the executions did not end there. Contrary to Edward's orders, 42 Lancastrian knights were taken prisoner. If their captors were hoping for ransom they were to be disappointed. Edward was merciless, and ordered that they too should be beheaded.
Whether or not this is the
best course of action for Dany is another question, but there are clear historical parallels at work here.