I've heard it strenuously claimed from multiple sources that the most important exercises for the elderly are not strength-focused but balance focused.

There's a path from falling to bacterial pneumonia that, as one person put it, means that "The death certificate says the cause of death is pneumonia, but the real cause of death was falling."

I'm fuzzy on the degree to which HIIT would contribute to lower incidence of falling injuries. Meanwhile I have a large pool of anecdata about yoga and taichi, some of it first person (I have, in the last five years, tried very hard to break my own ankle on several occasions, but walked away without even a sprain).