But the delta-normal implementation is clearly not appropriate for portfolios with heavy option components, or exposed to few sources of risk, such as traders' desks. Other implementations of VAR do allow asymmetric payoffs. A third, more specific, point is that the VAR approach is useless because volatilities and correlations change over time. This is debatable. Even when changes occur, the degree of precision in daily volatilities is much higher than that in expected returns.
Traders routinely take positions based on views that are even less reliable than risk measures.
Even better, we can use risk measures implied from option data, which are the best forecasts one could expect. Nassim Taleb also discusses a more general issue, which is that of the usefulness of scientific improvements. Admittedly, VAR is not perfect. However, our world is constructed by engineers, not physicists. In fact, risk managers are less concerned about precision than traders who have to price derivatives.