Those are actually pretty big moves. e..g, 120 to 72 2002-2008 means that a $100 bill in a drawer lost 40% of its general purpose purchasing power relative to the other currencies in the world, all of which presumably also had some inflation.

Wow, so you're saying that from 2008 until today, the purchasing power of the dollar is up relative to the other currencies of the world by about 40% (72 to ~100)? That's a pretty strong move, isn't it?

For example, the standard deviation of the Canadian dollar versus the euro is about half the variation of USD/EUR or USD/CAD.

Well, the laws of arithmetic make this almost inevitable. That's because the US$ is [still] the big reserve currency, and thus when it rises, it tens to rise against almost all other currencies, and when it tens to drop, it drops against almost all the other currencies. So if the US$ is rising against the EUR and is rising against the CAD, the laws of arithmetic will show that the CAD versus the EUR must have less volatility (variation).

These aren't just theoretical effects. I switched my [huge] mortgage to be in dollars while it was high, and switched it back to euros when the dollar was low, reducing the balance owed by half with two trades. (not that I'm so perfect...I did a whole bunch more similar changes in the subsequent few years that amounted to very little net gain)

If you can trade currencies successfully, you can definitely make all sorts of advantageous moves. Many years ago I knew a guy that worked for a national bank and traded currencies for them. By the end of his career there, he was trading portfolios of multiple 100s of millions of US$ equivalents. It's a crazy business though, he traded for small fractions most of the time, but made a bunch of money for the central bank each year. And they paid him a pittance relative to his gains.