As best I can remember, the dandelion was chosen because of its resilience, its ability to flourish anywhere, its uncanny way of popping up in places where it is least expected, and because no clan or other association uses it as their badge.
Some of us have silk dandelions that we wear as cap badges, and some others use real live blooms which they pluck from the ground.
The yellow bloom form of the flower is the one we use as a badge, but there is no reason why the white-fluffy stage of the flower couldn't be used as well.