6012 is a AC or DC- rod only according to Lincoln Electric (not DC+ as you claim everything is +) 6011 ,a fast freeze rod, which according Lincoln is good for deep penetration or sheet metal work. What's the difference? Current and polarity. 6010 is a deep penetration rod for use with DC+
You might wanna brush up a bit with this link
Not true (6012, 6022 are rated for AC/E- )
The amps are pretty much scaled for rod diameters. But 6013 run in E+ will have deeper penetration than 6013 run in E-.
Don't put words in my keyboard (so to speak). As I said before,flux is an important component to welding, but won't influence penetration (which was the original topic) nearly as much as amps & polarity E+/E-. Polarity, amps, and rod diameter (sized to the amps) are the most important with regards to penetration. And the topic of the original post, which was electron flow vs. current flow vs. penetration.
Using your logic, in DC welding you would just need a welder with one polarity, one amp setting, and use different rod flux to vary penetration.