Coming in late on yet another thread...but just my 2c. In my style, we tend to do a lot of bag work, using square bags with partners, ie holding them against our bodies while the other kicks, and heavy kick bags in our own time. In basics we're taught to keep that foot straight, but when we're actually trying to knock someone back (not push, but drive), we're taught to let that foot turn. It's not something that happens before the technique, where it would telegraph, but something that happens during it. The rear hip drives forward, letting the rest of the body contribute its power, not just the kicking leg and the muscles contracting up the front of the body. I'm quite a flexible guy, so that's not the issue here, it's just a simple case of being able to drive the bag holder back more effectively if you let the foot turn (to about 30-40 in my case). There's one thing that may (or may not ) give you a slightly different perspective on the images taken from jwt's video. In it, assuming that a zenkutsu-dachi is the same in both our schools, as the back foot slides through, the stationary foot would have turned slightly, as noone (I think) practices that stance with both feet parallel. On top of this, our hips drive that oi-suki through, so for an instant at least, the hip behind the striking hand is in front of the other. This is basically the same effect found when a kick is fully extended. One final thing, many people would probably find that your "natural" standing stance consists of having both feet pointed slightly outwards, so why, when applying force to those joints in something like a front kick, would you restrict the knee joint by forcing that foot in when it's not its natural position? Food for thought anyway
I've learned various forms of front kick with varying degrees of pivot in the supporting foot. My "default setting" is about a 45-degree pivot as others have mentioned. Probably no coincidence that I'm a big fan of muay thai, lethwei, etc. I think it really depends on the intent of the kick though. The teep is a thrusting action, so the hips come into play. A snapping action may not benefit as much from the hip range. I was taught one variation on a front kick where, not only do you not pivot on the supporting foot, you keep your supporting foot pointing inward in a pidgeon-toed stance. To me, that felt extremely unnatural. But it shields the groin a bit. It was a kickboxing class, but the teacher came from a karate background. Don't know how representative that is. My only other experience with karate is 6 months of Shotokan, which certainly didn't kick that way.
Of course, I definitely agree that with a snapping front kick you wouldn't extend the hip/turn the foot, only when you're looking for more power from the back leg, or I guess if you were teeping/holding someone off with the front leg
From a sparring perspective. I'll only keep my supporting foot facing forward with a snapping front kick where it's not about power, so I'll try to keep my telegraphing motion down to 0% and just throw it out of nowhere. However when I want to put more power into the front kick, it's not just about loading/setting up, it's also about range. The range on a front kick is a lot shorter when you keep the supporting foot facing towards your target, but when you open up your hips your range increases and you can kick through your target which translates into more stopping power. If you're close enough to kick through your target with your supporting foot facing forward, your opponent can punch you in the face which kinda defeats the point of going for a kick. Of course this really depends on you and your opponent. If you're tall and you have long legs, you can probably get away with it if your opponent is shorter than you, but I wouldn't recommend it even if you're tall. I'm 5'7 in a country where the average height is 6ft, so for me it's important to make full use of my range, but there's no reason tall people shouldn't either.
