Just to make the discussion more interesting, I'll play devil's advocate and take the opposing point of view :
Maybe it's the case that in the long run, the explosion in IV on down moves, which happens 5% of the time, will compensate for the loss of premium and commission the other 95% of the time?
That's because it's not just IV, there's also the sensitivity of the IV to a change in price and to the level of IV itself, aka vanna and vomma. vomma is to vega what gamma is to delta, a 2nd order effect.
Instead of theory, see this article for a concrete example:
http://www.optionworkshop.com/read/vanna-and-put-explosion
Here, an increase in IV of 17% resulted in an increase in the Put price by 163% ! As the author writes, "the point I want to make is that when tension enters the market, the OTM puts literally explode in value. Very simply put, when IV rises, the effects of Vanna and Vomma blow up the OTM putâs premiums, deltas and vegas in a way that looking at a simple risk graph cannot predict."
Also, the way you put it, "a 50% change in IV results only in a smaller change of the Put value" makes it sound as if a 50% change in IV is a big deal. But here again, we are talking about a 2nd order term, the volatility of volatility, for which 50% is not a big deal. See a chart of VVIX against the VIX, for example.
http://www.barchart.com/chart.php?sym=$VVIX&t=BAR&size=M&v=0&g=1&p=D&d=X&qb=1&style=technical&template=