@William Gilmore, CFA:
The key point here is that we know very well how to reduce volatility or, more generally, variability in a time series of returns and thus bring the geometric mean closer to the arithmetic mean if we manage to keep the arithmetic mean constant: Through diversification.

The difference between the arithmetic mean and the geometric mean is part of a more fundamental property of dynamic systems known as non-ergodicity (i.e. the difference between the ensemble average and the time average). Markowitz's famous 1952 result points into the right direction, but he never really understood the ergodicity problem and its implications. In fact, we can find a temporal analogue of his ensemble average result for the multi-period decision problem of individual investors as outlined in footnote 1 of my paper ‘Sharper Than Sharpe: A New Portfolio Measure’ publicly available at SSRN https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4823752

Volatility, or more generally the variability of period returns, does play an essential role for investors as it directly affects the optimal weighting (or leverage) of a portfolio (cf. the Kelly criterion). The term “volatility inflation”, on the other hand, would only make sense if investors would be interested in the arithmetic mean as the determinant of the terminal wealth of a multi-period return series, which is simply not the case. Remember that it is G = A - VD what investors care about and not A = G + VD, where VD is defined as the variability drag (the degree of the non-ergodicity of the problem).