That's interesting, I've always had the impression that southern Germans have really disliked Prussia, Prussian domination of Germany, the modern city of Berlin

etc. Would you say that despite of all this Frederick the Great is still a well respected ruler in the south, and even southern German players are fine with Prussian Germany and don't need no Bavarian (or Badenian) dominated Germany?
Well, that's acctually not that easy to answer. Culturally Prussia certainly does have some kind bad reputation in the South, especially the so called "Prussian values", i.e. strictness, discipline and order (I'd say non Prussians consider themselves more "relaxed" on that front.

) The atrocities during WW2 are also wildly associated with Prussia, although obviously all German states share their burden here. Most Nazis in American Movies act and speak like typical Prussian soldiers too, by the way. "The name "Prussia" is not used in Germany anymore, because a lot of people associate it with the Nazis and the crimes they have commited.
On the other hand, especially under Bismarck, Prussia united all German states and forged Germany as one of the most important and ecomomically successful countries within Europe. Most German states suffered hugely during the "30 years war" in the 17th century, because they were too weak to defend themselves against counties like France or Sweden. A united German nation state therefore was desired by many.
Furthermore, what used to be called Prussia, is now one of the poorest and less densely populated regions within Germany, especially due to the Sovjet occupation after WW2 (now called Brandenburg, which used to be the Prussian heartland around Berlin). So it doesn't feel very "threatening" anymore, if you know what I mean?
So in my opinion, if you want to pick one state instead of the HRE or Germany, you have to go with Prussia. The other states like Saxony or Bavaria never were remotely as important or impactful as Prussia was for German history (for good or bad), that is just a fact, you can not ignore.
Bonus question: if you had to choose one leader (doesn't have to be a political leader) "leading" "Germany" in the 18th or 19th century, who can't be a Prussian ruler or Bismarck or kaiser, who would that be?
I guess I would go with one of the revolutionaries of 1848. If they had been successful, the German and European history could have been much different (and less violent). I'm not an expert here, but I guess Carl Schurz, Robert Blum or Emma Herwegh are proably among of the most popular figures there.