We prefer you to practice basic awareness during walking meditation because the body is moving. Therefore it's more dangerous to yourself and other beings to get involved in thinking about other things. So we prefer not to do reflections during the walking meditation. Unless, of course, you are indoors with no obvious problems, and that's the only time you have to do it.
However, a lot of the times we see that during our normal lives we are thinking a lot. So, learning how to get into the body and into the present moment, this is a major benefit of walking meditation. To get into the body, to come into the present, to let go of those thoughts. To let go of the restlessness, to just be here, that's a great strength of walking meditation.
It helps to tie your "dropping into the present", more and more, throughout our normal life - because we usually live very busy, busy lifestyles. Learning how to just drop into those moments where nothing is happening, where we don't have to do anything, is very helpful.