I understand the stepping thing when you are talking about actually moving your feet, but what about when you are turning 180 degrees without moving your feet as you would do for a happo-giri? it seems very unwieldy to pick up each foot and put it back down again for this movement, unless you are jumping, which has its own problems.
you need to pickup your feet. we practice weapon works outdoor wearing shoes. we practice on uneven grass surface (slippery as hell in the morning dews) and on asphalt. you learn very quickly that the footwork on smooth tatami surface doesn't work well here. the trick is to soften your hips or the kua (in chinese term) along with the knees and ankles. stiffen those and you are in for a very painful practice.
if you know a taekwondo person, ask him/her to do a spin back kick, then watch their feet.
and yes, you need to understand aiki.