But there is not that much sunlight at the poles, which is actually the reason why there is ice. Also, the antarctic ice coverage seems to be pretty stable.
Depends on the season, in summer with 24/7 sunlight the Arctic takes more heat than a location near the equator.
Apparently the Arctic gets more insolation than the Antarctic, but the former only peaks at about 25% higher than the Equatorial mean, and the peak is relatively short.[1]
You might want to read what you link: Because the insolation function is the same for the northern and southern hemispheres, i.e., S˜(φ,ε)=S˜(−φ,−ε), annual solar insolation is the same for corresponding latitudes in each hemisphere.