But not the speculation around the lack of his execution led to the stigma which labeled him as a traitor, although it was part of it.
Kossuth - as I mentioned - went to emigration, on August 12 he sent a letter to Görgey explaining why he gave up the power to him and with more reproach, on the 17th he crossed the Ottoman border with his brain grinding over the events of the past year, and not a month later he sent his so called Letter of Vidin to the diplomats in England and France, to the emissaries and ambassadors of the Revolutionary Government still staying in foreign countries, so they have something to ask help with from the western powers. His goal was to demonstrate that not the weakness of arms but treachery led to the downfall of the Revolution, he wanted to give hope for a restart and explanation. The letter ofc reached Hungary too, probably was intended, so it was designed to revitalize and dispelling doubts in our strength. I read it and I also see a mind which tries to rationalize how they could lose from the sure position of '49's spring.
In this letter he recaps the events, and how Görgey sunk the morale of the army. How he managed to tie the officer's loyalty to himself, how they nurtured royalist sentiments, how they spread hopelessness, how they wasted lives and resources, how avoided combat when they should have and entered unnecessary fights when they shouldn't, how they conspired with the Peace Party, and how they continuously parleyed with the Russians. And as a closing accord he reached for military dictatorship, and how he pressured Kossuth with the help of several ministers to give up the governorship, and then laid down weapons before the Russians.
Kossuth was also surrounded with people who had little sympathy for Görgey, like Perczel and Dembinski, their voice was also heard, and many others who hopped onto the bandwagon and found faults in Görgey's decisions and moves throughout the whole War. Came the "what if" scenarios, which discussed up to this day, and almost as popular here like the similar exercises related to WWII, which Bernd is familiar with.
Following the years of the War Görgey being a traitor was a prevailing view, as a reply he wrote the aforementioned book, the Mein Leben und Wirken in Ungarn in den Jahren 1848 und 1849. This offered his side of the story which not just added shades for the question, but many veteran decided to absolve him and declare him as not traitor.