You're missing a number of points and writing what it seems you want to be true: that the 4% figure "is based on multiple studies that included using Monte Carlo analyses". It wasn't.
If what you meant to say is that subsequent Monte Carlo simulations validated this figure, then there's a different problem with the narrative. Because that would also validate the use of historical data - something you say has an intrinsic shortcoming.
Of course the odds are virtually nil that the next thirty years will match a previous thirty year period. Just as the odds are virtually nil that the next thirty years will match a performance pulled out of a hat (aka a Monte Carlo iteration). This is a red herring.
In the typical Monte Carlo simulation, patterns are abstracted away. You seem to regard this as a virtue, writing disapprovingly that historical returns are used "sometimes in the precise order in which these returns were registered." (Orderings weren't preserved merely "sometimes" but always when Bengen came up with his 4% figure. See his
original paper.)
Again I suggest reading the AAII piece. You'll find a concrete example of how ignoring some patterns can affect results. Bengen notes there that if one rebalances much less frequently than yearly, " you can actually add about a quarter of a percentage point to your withdrawal rate" He attributes this to persistence of performance. That's a kind of pattern that simplistic Monte Carlo simulations abstract away.
"Monte Carlo simulations continue to grow in popularity." When all else fails, cite popularity for validation. I'm sure VHS's popularity meant that it was the superior technology, that
the more popular Windows is better than Mac, etc.
There really was some interesting stuff that you didn't discuss. Like how "there is an inverse relationship between the long-term valuation of the stock market and how much retirees can withdraw without running out of money."
How does that historical data fit into your Monte Carlo simulations? How do you map
CAPE into means and standard deviations for large cap stocks, small cap stocks, and bonds? Those are the inputs for the simulators you're linking to.

I think Monte Carlo engines are fine tools. Just so long as they're not simplistic, matched to the right task, and employed by knowledgeable users. Used as you suggest, they have lots of issues.
There are no constraints to Monte Carlo simulation, only constraints users create in a model (or constraints that users are forced to deal with when using someone else’s model). Non-normal asset-class returns and autocorrelations can be incorporated into Monte Carlo simulations, albeit with proper care.
David Blanchett and Wade Pfau,
The Power and Limitations of Monte Carlo Simulations, 2014.
https://www.advisorperspectives.com/articles/2014/08/26/the-power-and-limitations-of-monte-carlo-simulations