HIIT is supposed to take everything you've got, you should limp home from it, and be in a bad mood the rest of the day. You could do it at the end of a ride, but why ruin an otherwise pleasant time on the bike?
But for context, I'm a natural sprinter, and realized that HIIT wasn't doing me any good so I stopped doing it a few years ago. Better to train your weaknesses than strengths.