For kicking, punching or in general?
In my opinion generally, it depends on what your doing. As people said there are advantages to both. The most common way of standing and moving is on the balls of your feet because theoretically you are more mobile with your weight on your toes already loaded up to move.
Better explanation in this video at 2:43...
However there are many instances in which people effectively use heel to toe footwork. If you look at any good boxer/thai fighter most likely they are neither always flat-footed nor always on there toes. Some examples of heel to toe can be seen in this video at various points.
As for during kicks if you watch the video of Bas I think the main point he was trying to make is that your not gaining power through your pivot but rather your pivoting due to the moment of your leg. So when you step out to kick you can turn your foot to the position it should be in, stand flatter, and completely follow through with your kick. Standing flat footed has the advantage of being more grounded so you can throw harder.
But the down side is if your kicking pads thats all well and good but in real sparring/fighting there is truth to the fact that being on the ball of your foot if you get caught off balance or throw a bad kick can save you from potential knee injuries. I have bad knees so I try and stay a little bit more on my toes but i remember to focus on that step out and using the tension in my hips to generate power rather then emphasizing the pivot.
Edit: Sorry don't know how to embed