Another problem with your analysis is that there was no such thing as a Dow index stock (or ETF) in 1932. The Dows is an index that is currently comprised of 30 publicly traded companies most of which were not part of the index back in 1932.
This is the list of the Dow components in 1932:
Allied Chemical
General Electric Company
Nash Motors *
American Can
General Foods
Procter & Gamble Company *
American Smelting
General Motors Corporation
Sears Roebuck & Company
American Tobacco B *
Goodyear
Standard Oil of California
Bethlehem Steel
International Business Machines *
Standard Oil (NJ)
Borden
International Harvester
Texas Company
Chrysler
International Nickel
Union Carbide
Coca-Cola Company *
International Shoe *
U.S. Steel
Drug Incorporated *
Johns-Manville
Westinghouse Electric
Eastman Kodak Company
Loew’s *
Woolworth

Many of these companies no longer exists, and even some that still do, have been though bankruptcy which mean that the shareholders were wiped out.

Still, Gold is considered a wealth preserver not an investment.

Had one bought the Dow index as stock in 1932, denominated in US dollars, that stock would have appreciated as an asset from $40 at its low, to $8000 today, which is almost 10 times the dollar return of gold (had one been really fortunate or very good at trading, that stock could have been sold for $14,000 in 2007, but that is a different story). In addition, dividends on the Dow index would have returned another 5% annually on average, which over 80 years provides another multiple return of 32 times, using the Rule of 72 for compounding. This makes the total appreciation of Dow stock, 32 x 200 = 6400 times return while gold returned 40 times. The reason for this discrepancy: Gold is a non-productive asset and does not generate any dividends or interest. In fact, physical gold must be stored and protected and can actually cost from 1-2% of its value every year.

So, the long term (80 year) case for gold is very poor. Even a high degree of inflation will be adjusted over time by equally higher wages (wages are a component of inflation, after all). Other assets, like real estate, commodities and stock will also adjust to offset the effects of inflation over time. But I do acknowledge that there is a prospect of inflation in the near term that might provide a case for gold as a Speculation. That is much different than gold as a diversifier.

I do not begrudge anyone their pleasure. If owning gold gives pleasure, then buy some. But it should not be mistaken as an investment because it is not. We are just now getting into a position to have something of a repeat of the 1932 to 2007 equity scenario after suffering the greatest economic decline since the Great Depression. Now would be a great time to put everything into stocks. And if one is worried about inflation, skew the asset allocation towards Basic Industrial Materials, Energy and Ag Commodities, all real assets which will appreciate at least as fast as inflation.