Some Nazis were indeed left-wing and Socialist. Goebbels was very left wing, and most of the SA were leftists, most started out as Communist street brawlers.
Which was one of the reasons Hitler had to do away with them to gain the trust of the German business class, who was more scared of Bolshevism, than anything. Hitler was much more pragmatic than most in the Nazi Party. But the original name of the Nazi Party was the “German Workers’ Party”
Actually, no - NAZI stands for "National Socialist German Workers Party" in German (Nationalsozialistische Deutsche Arbeiterpartei) - so why deliberately exclude the crucial "National Socialist" part that was always there?
As well, the association between socialism and the "workers" has been consistent worldwide, so that hardly breaks the Nazi concept away from socialism.
Leftists have labored long and hard to deny the link between socialism and Nazism, an astounding effort at all, given that Nazism IS socialism in it's truest form.
I for one think that link needs to remain as clear as possible.