I don't understand the purpose of the max. Why don't we add the square roots together instead so you have an idea of both dimensions? And hence an estimation of the entire area in texture space?
I did a little research into this and tl;dr square mips don't work well with very narrow quadrilaterals if you use an area measure and max is used since overfiltered images look better than underfiltered ones (see page 7). This is all predicated on the fact that mipmaps rely on symmetrical prefiltered mips and so we can only pick one level for both dimensions (see page 3).