I regularly look at the ADR (average daily range), the ATR (average true range) and implied volatility. Usually historical volatility works well as a reference, but there are some periods (such as holidays or end of year), where you cannot use historical volatility.
This is what I use the average true range / average daily range for:
-> calculating money management stop loss
-> displaying seasonal volatility intraday
-> defining trailing stops or MAE (see SuperTrend indicator)
-> establish volatility targets for the day trading session
I do not see any advantage of replacing the average true range with a standard deviation. The standard deviation confuses direction and volatility. Direction is a higher timeframe volatility, so it measures two-dimensional volatility.
If you have a chop market with high volatility going nowhere, the standard deviation can actually be small, although volatility for this time frame is high. The standard deviation does not tell me a lot. This is one reason that I do not use Bollinger Bands, but go for Keltner Channels. Easier to understand what they mean.