The DM generally hast the most information too, so that makes sense.
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what is reasonable is what follows from actual reason / logic and real world experience, and applying that to a hypothetical and fantastical situation.
Let's call the situation S. Let's call the range of reasonable outcomes R(O). It's true that S constrains R(O). The point that
@hawkeyefan has made, and that I have also made, and have illustrated with my post 1891 upthread, is that - in a game of imagination - S can be varied. And the possible variations of S obviously, and very significantly, relax the constraints on R(O).
Now if the GM has some S in mind, and does not want to vary that, that may be the GM's prerogative (at least at some, perhaps many, tables). But a GM who does that, therefore forms the view that the player's desired outcome falls outside R(O), and therefore tells the player that their desired outcome
does not come to pass is not enhancing, or increasing, or even upholding, player agency. They are exercising their own agency as author of the shared fiction. In particular, they are insisting on their own authorship of S as they have envisaged it.
This is a very GM-driven style of RPGing.
A quote from an earlier post:
'looking for a reason to say no either, we just take the reason we see as the most reasonable one in the circumstances'
As Pemerton says, can a bunch of misfits (Aragorn, Gimli, Legolas) with no real proof of heritage, be able to convince a noble to give them treasured horses as the most reasonable outcome? Or more likely the three would taken prisoner / executed?
Here, I think most reasonable is a bit extreme, and still very subjective, question is whether people think the above is a reasonable outcome, regardless of whether most likely to occur or not, and how much flex a DM will give in such a situation.
This is one reason why early editions of D&D (and some other classic games, eg Traveller) include reaction tables - there is always a chance of an enthusiastic reaction, such as Eomer's to Aragorn.
I personally prefer to reframe the reaction outcome as a resolution of a player's declared action (eg
to make a good impression, by announcing lineage and loyalties). But by using dice rolls ("say 'yes' or roll the dice"), the full range of interesting possibilities is kept open.
I am not the biggest fan of fiat abilities, because I think dice rolls produce a more compelling pattern of success and failure (Robin Laws calls this the pass/fail cycle, and suggests that it is inherent to all stories). But where fiat abilities are tightly rationed (eg as is the case for Prince Valiant Storyteller Certificates), then they allow the player to really stake their claim -
This is where I care, and will produce the outcome I want!
In the context of 5e D&D, the "rationing" consists in being able to choose only one background, and having the fictional circumstances that enliven it be reasonably narrow. I think this design is less compelling than Prince Valiant, as the player makes their choice at the start of play and in anticipation, rather than at the moment of truth as happens i Prince Valiant - but this would just be one way in which D&D design tends to favour "comfortable" over "compelling", and probably not the most invidious.
Ultimately I like to resolve these things through the rules. That's what they're for. If something being attempted is flat-out impossible (eg we have already established the duke is out of town) then no roll takes place - although you may be able to get an audience with his cousin, butler, etc. But if there is even a chance of a particular approach working, even if it's not the most likely outcome, then that's what the dice are for - play out the scene then make a Persuade check against the efreet/king/butler/secret service agents.
See just above - 5e isn't designed to best fit my preferences; but given how it presents backgrounds, I don't think it's particularly hard to make them work.