If we're familiar with high intensity interval training, we may be aware of its effect on aerobic capacity as well. HIIT is basically an anaerobic challenge. Ironically, the greatest improvement is with aerobic capacity.

The point here is that the belief that some activities rely on anaerobic capacity is in fact incorrect. HIIT can be seen as the activity most dependent on anaerobic capacity, so why does it improve aerobic capacity more than other activities believed to rely on aerobic capacity (therefore train this capacity), i.e. low intensity long duration?

The anaerobic/aerobic premise is flawed. All activity relies primarily on aerobic capacity.

This ain't what's going on with short term ketogenic challenge. Instead, it's likely some adaptation - a shift - of a different set of mechanisms and pathways needed to digest, absorb and metabolize fundamentally different substrates - carbs vs fats, glucose vs fatty acids. In chemistry, this would be like swapping out all the base chemicals we don't need, and put in all the chemicals we actually need. In chemistry, this is easy, it's just a bunch of vials and bottles and whatnots, just plug and play, get running next day. In biochemistry, the "chemicals" must be made on site. This takes time. During this transition period, output invariably suffers. Once adaptation is complete, output goes back up. 4 days is right smack in the middle of this period, where output is at its lowest. There's a great analogy with an oral glucose tolerance test, where we don't measure before the 2 hour mark, where blood glucose would certainly be sky high, where it would clearly indicate diabetes, if we were just retarded enough to conclude that.