I admire your effort and thoughtfulness, but one of your key assumptions is wrong and changes everything, that being you treating each year's return as independent. There is a great deal of autocorrelation in the market. The tendency is a return to the mean. I haven't done an analysis on this, but it's not necessary to illustrate the point. In your example, it is possible for there to be three consecutive years of gains of 30% or more three consecutive years of drops that much or greater. A single year of a gain or drop that large is rare but happens sometimes. However, because we are describing a real world system, it's not accurate. People do not magically come up with 30% more money year after year, nor do they continue to pull out 30% of their money year after year. The market "wants" to stabilize around that 10% figure, so the tendency is for there to be a low return after a high return year and a high return year after a low return year. If you reran your simulation using a dynamic model of some kind that accounts for autocorrelation, you would get markedly different results, like radically different results.
Also, I would argue that using data prior to 1950 is probably not best... The world is so much different in the post internet era. Money moves faster, the FED moves faster, there are more regulations, etc.
I am still young (33), but I plan to have multiple income streams when I retire (equities, real estate rentals, my own business, etc), so this isn't as much of a concern, but I would still argue that the best strategy would be to have a large portion of your wealth in a broad market index fund, some money in bonds, and a 3-6 month emergency savings account. Ideally you're not really worried about increasing wealth by the time your retire, just preserving, so I do agree that minimizing risk (within reason) is wise.