I have no problem performing at high intensities on very low to zero carb diet in terms of energy, but I find I do not maintain a good body composition over time doing so. I was practicing martial arts (black belt level) 3 days a week until last summer when I cut it out except for once a week and opted for 4-6 mile run/walks instead for the same 3 days a week. Much lower intensity stuff. I dropped some fat along the way. This was all while concurrently strength training through the whole time. I tend to now think that for me, HIIT is somewhat catabolic and stressful when done more than once a week.