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

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.