Having plowed through 1750 posts in this thread over the last week, I now have a much better understanding of the "4% rule". Thanks everyone who's contributed!
My personal reflection on the questions and misunderstandings around the rule is that when you're dealing with probability and statistics, it's very important to be very clear about what question you are asking. A while back someone asked about the apparent contradiction about retiree A and B where A started one year and B started the year after when the market had dropped and why retiree A could withdraw more money than B.
The way I like to think about it is that you don't have a 95% chance of a 4% withdrawal rate succeeding. What the analysis said is that out of all starting years, 95% of the years succeeded. So, assuming the future is substantially the same as the past, if you retire at a random year in the future you have a 95% chance of picking a year that succeeds. But you retire in a single, specific year, and your retirement either will or will not succeed. It's not random, you just don't know which the outcome is going to be yet.
But, when you start saying things like "retiree B retires after a 20% market drop", you've explicitly conditioned your question and the answer is no longer that 95% of the years would succeed, because most of those years didn't start with a 20% drop. You'll have to restrict yourself to the situations in the past that match your condition (if there are any, there's not much data and I suspect you'll quickly run out of data if you start matching on other variables.) The same applies to any other present-day knowledge you are attempting to condition on, like the CAPE someone mentioned, inflation rate, whatever.
So when people are saying "I'm going to go with a 3% WR because valuations are so high", or whatever, it seems they should calculate what the SWR for the years in history that match that condition. Or, "I'm going to go with 6% because I can lower my expenses by 25% if (condition is fulfilled)", or "because I'm getting x$ in SS in 15 years." Those hypotheses are all testable against the historical data. I agree that flexibility in expenses and income are crucial for peace of mind, but assuming that the data exists it seems much better to actually calculate what the expected results are than to just handwave and assert that it should be fine.
Anyway, just my impressions from all this reading. Thanks again everyone.