Technically, the rules don’t say a DM can’t just say “the goblin intimidates you. He succeeds without needing to make a check and you hand over all your gold”, but doing so would be contrary to the guidance the rules offer on how to determine the outcome of an action, so the DM would not be well-supported in making that call.
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...
Rolling with it and ignoring the dice are called out as having drawbacks, while balancing between the two is not.
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).
To bring this back to the topic of actions meant to force a PC to make a specific decision, I think the “roleplaying rule” provides us with guidance on how the DM ought to determine success or failure in this situation - the player decides what their character thinks, feels, and does, so in the absence of more specific rules governing the resolution of a particular action, the DM is advised to let the player decide whether an action that would cause their character to think, feel, or do something succeeds, fails, or requires a roll.
While I agree in general, I would also like to insist on the fact that sometimes it's normal for players to be forced into doing something, because it's magical, although - usually for scenario reasons, it might not be obvious at that point. Encounters with Aboleth of Elder Brains or dominating vampires can certainly go that way, and players slamming the door for "losing their player agency" are absolutely welcome not to come back at our tables ever. I think lots of players (at least on these forums) have become way too oversensitive about what is, in the end, only a game. So, when in doubt, in a magical world, you might just want to assume that it was magic rather than a misguided use of an ability score. You trust your DM, right ?
