I think you're missing something important in your analysis, and that is the fact that ice isn't 2 dimensional, but 3.
Ice volume is also very important in how resistant it is to melt, and correlating extent and area to melt isn't going to hold on for much longer if it held up at all.
Yes, but that third dimension, thickness, is several orders of magnitude smaller than the other two. Hence, the third dimension forces have much less influence on the total makeup than the other two.
I think you misunderstand me, the issue isn't that you should take all three separately, but that you should use volume, or perhaps even better, density.
Conversely, the third dimension cannot go to 0, without the extent going to 0. The extent will change based on the dimension which has the greatest influence. The factors influencing thickness, like wave action, are small compared to those acting on the overall area, sunlight and seawater. Thickness changes does not drive the sea ice, rather they occur through these other factors.
While technically this might be true, the volume of sea ice can tell us a lot about how resistant it is to melting. Thick compact multiyear ice is much fresher (has less salt), much colder, and generally more resistant to melting than say slush even though they might cover the same area.
And the reason I suggested 'density' was because volume only gives the total 3d space the ice occupies, not how solid the ice is in that 3d space. Using the example I said above, everyone would agree that said thick multiyear ice is far more resistant than first year ice that might have the same volume.