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> That's right, it averaged out to net zero over more than a century.

It just averages out because you selected an arbitrary period, which makes the point essentially meaningless. Id didn't average out from 1800 to 1900, from 1814 to 1914, from 1800 to 1850 and so on.

> It's a fundamentally different behavior, both in direction and magnitude.

Again, this is not correct. If you look at the actual data, you can see that the the inflationary periods in the 20th century actually have smaller inflation per year than those in the 19th century. The fundamental difference is the absence of severe deflationary crises, of which there were plenty in the 19th century. The top ten highest inflation rates of the last 200 years were all in the 19th century. Have a look at the data: http://www.in2013dollars.com/1800-dollars-in-2016