I agree with your points about jogging, sir. It may be because I was the captain of the cross-country team when I was in high school (read: I trained my mind from a young age for endurance), but I just can't get into HITT.
From a mathematical standpoint, HIIT does burn more calories than steady state, but not as many as is advertised. I'll link to a video that breaks down the theory and math a bit more...but because it's a long ass video, I thought I'd give some cliff notes so that we can all have something to argue about.
I'm about to use FAKE numbers, for the sake of argument: Let's say most people do moderate intensity when they jog (HR = 130 bpm). HIIT has peaks of high intensity (HR = 180 bpm) and valleys of low intensity (HR = 90 bpm). For arguments sake, let's say that we burn 10 calories a minute with MISS, 15 a minute with HIIT (peaks) and 5 a minute with LISS (valleys). Let's also assume you do 1to1 peak-to-valley HIIT (which most people don't) and then let's factor in the afterburn concept.
40 minutes of MISS = 400 calories burned plus 28 calories for 7% afterburn = 428 calories.
30 minutes of HIIT = 300 calories burned (15*15 = 225, 15*5 = 75) + 42 calories for 14% afterburn = 342 calories.
So, by doing 10 extra minutes of MISS, you burn more calories total. Here's the full video is you're actually interested...I found it fascinating.
HOWEVER, that's just theory and math and doesn't take other things into accounts, such as muscle stimulation, glycogen useage, metabolism effects, etc. This was just purely food for thought, since I found this particular video so interesting.