Ok. So then it is possible to be able to generate full power from the stances eve if you are not in a full stance as long as you are rooted and have properly practiced your stance work?
I guess that begs the question, what is a full stance and what is a "not full" stance?
People in training will often use a deeper and/or wider stance than they would use in actuall fighting. The training stances are meant to build strength in the legs and (hopefully) develop your ability to root if you are doing it correctly. But as was stated above, mobility is important so in a real fight you might not want to be so low and deep.
If you learn to do that in training, you should be able to apply the root in a less deep, and less wide stance. The stance itself is sort of an ideal position, and that's why we train with it. But the chaotic reality of combat may prevent you from hitting that ideal stance. So you do the best you can under the circumstances, and you apply your root nevertheless. The bottom line is, if your feet are floating, you severely reduce the power you can deliver in your technique. As was said above, try shooting off a shotgun while standing in rollerskates.
I think that someone who doesn't fully understand how to root will, as I stated previously, just sink straight down. When throwing a punch, they tend to throw their body forward into the punch, to get that body mass behind it. This can actually be fairly effective if done well. But it's better to root in your stance, keep your body neutral between your feet, and use your rear foot to drive down into the ground and torque thru the waist to pivot and deliver the punch forward. But when I say pivot, I don't necessarily mean pivot into a different stance (some systems do, others do not, and sometimes it depends on the circumstances). Rather, root in and keep your stance, but pivot thru the waist and hips to drive the punch. Don't lean the upper body into it. It takes some time and dilligent training under a teacher who understands this. But in my opinion it has the potential to give better results in the long run, tho it may take longer to really "get it".
regardless, tho, I think getting a stronger sense of being rooted will help what you are doing, and that is what is so important about stance training.
Getting back to your original post, go back and practice your form again, using clean stances as you understand them, but apply the rooting in every single movement and every single stance and the application of every single technique throughout the form. Go slow and make sure every part is right. Do not rush thru it or you will get sloppy. See how that makes you feel in your form. I bet your lower legs and feet will be much more fatigued until your strength and rooting improves. But you should also feel a noticeable improvement in the delivery of power.