Just pointing out that, actually, he is well supported: "With this approach, the DM
decides whether an action or a plan succeeds or fails based on how well the players make their case, how thorough or creative they are,
or other factors."
Note in particular the use of the words "decides" and not "determines", although that is used in the previous sentence "determine success or failure as they like in other situations.". I know, it's only one of the two extreme approaches outlined in "the Role of Dice", but it shows that there is actually support for the DM just deciding whatever he wants without rolling the dice or actually even without mechanics. Once more, the rules are very open.
By the way, the "Ignoring the dice" is very much the way we play at our tables. This is not to say that we ignore the mechanics, but there is a lot of auto-success/failure based on descriptions of actions, and that for both the PCs and the NPCs (and their respective stats).
As for the "hand over all your gold", it's another matter entirely, it's not about the resolution mechanic, it's about what players find acceptable in terms of game situations. And yes, although it was a long time ago, some of us have been raised on dungeons where this happened now and then to characters and their magic items because of simple pipes or pools in rooms...
This is bit of a biased reading, both approaches do not have only drawbacks, they have advantages first and foremost, especially ignoring the dice, since the advantage is "This approach rewards creativity by encouraging players to look to the situation you’ve described for an answer, rather than looking to their character sheet or their character’s special abilities." which I consider a very good thing, compared to a disadvantage of " A DM might come to favor certain players or approaches, or even work against good ideas if they send the game in a direction he or she doesn’t like. This approach can also slow the game if the DM focuses on one “correct” action that the characters must describe to overcome an obstacle." because that is circumstantial and good DMs can usually avoid that trap (it's not something that we've had a problem with, actually).