You're going a little off the rails, blindly accepting economic formulas. Here's an interesting article about bitcoin volatility that proves you wrong: http://woobull.com/bitcoin-volatility-will-match-major-fiat-currencies-by-2019/
The way that you're measuring volatility is extremely one-dimensional. As you can clearly see if you look at the actual charts instead of arbitrary measurements of day by day volatility, you'll realise that the US dollar's fluctuation is held fairly consistently around the same range.
Bitcoin's fluctuation is based on trends because the price is only about how much people are willing to pay in order to hold the coin.
Sure, you can say that Bitcoin is becoming less volatile, but in the last few weeks it's rose from about $1200 to about $1800. The US dollar's changes have been barely noticeable. It's just not a comparable type of volatility.
Indeed, I didn't look into the numbers, but I have the impression that analysis only considered the high-frequency part of the volatility (say, daily or hourly or so). As you correctly point out, the low frequency volatility (weeks, months, years) of most big fiat is pretty small, and that of bitcoin is still huge.
For instance, over its 17 years of existance, the EURO and the USD never deviated more than something like 50%, going from an exchange rate of 0.8 to 1.5 or so.
Over its 8 years of existence, bitcoin did 6 orders of magnitude. Of course, that won't happen any more (1 billion a coin
I'm hodling in case ). But in 2 years time, same vol, don't think so. It doesn't contain any regulating mechanism !