Theoretically, numerically and empirically the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. Two factor models - one persistent and other mean reverting - do a better job describing simultaneously the high and low frequency dynamics of volatility - to explain both autocorrelation of volatility and the volatility of volatility.
Volatility is not constant. It is both time-varying and predictable. Gaussian quasi-maximum likelihood estimation (QMLE) for estimating stochastic volatility falls wayside because the volatility models are non-Gaussian - log absolute or squared returns. Range - difference of highest and lowest log security prices is a much more efficient estimator - due to its near normality.