Volatility, no matter how measured, is connected to (what academics call) price risk. However, almost everybody agrees that the higher the risk, the higher the returns can be.
Trend followers cannot make money in choppy, sideways markets, therefore they embrace volatility.
Even buy-and-hold investors are given ample opportunities to enter depressed markets or exit profitable trades in the presence of volatility.
Acute option traders can maximize their return by buying volatility via calls, put and other derivatives.
P.S.: I am not an advocate of short-term volatility trading that resembles gambling, especially when high leverage is involved.