> with bones and ligaments taking the peak power instead of muscles

That's kind of an odd way of phrasing it; I would have said something along the lines of them providing the upwards force through tension rather than bringing power into the discussion.

It's the time derivative of work, seemed natural to me. Also muscles use rate limited chemical reactions to move, so it is a reasonable assumption to model them as power limited (with different regimes for different metabolic mechanisms). So when talking about the limits of what a person can do with their muscles, power limits seem important.