The proof lies within your brain. Gotta look deep under those neural tissues of stupidity.
According to your explanation, Tsunade should have regenerated legs when she was soloed by a tree. Also, you should know that there is a difference between Madara's/Hashirama's regenerative ability and Tsunade's. If you're up to date with the manga, this should have been apparent.She grows a new body, until proven she can't. She can regenerate. Her chakra is in her head.
Madara grew legs