Perhaps, though it will probably be way easier when the player suddenly announces that he has an invite from the king as he did a favour to him earlier, before the game began! Could have happened, seems plausible to me! If you say no, you're railroading!
What's the issue with framing an appropriate check, here?
Are you saying that a successful check establishes the existence of the blacksmith? Because otherwise I don't see reason for any check here.
So are you suggesting an approach, where we roll dice to see whether the player gets to describe the things about the setting? Like if I want there to be a secret door, I roll perception and if I succeed there is? Or that if I want to declare that the mayor owes me a favour and I roll diplomacy and if I succeed, they do? Because that's not how D&D works or is designed to be played.
I think your examples are stated without regard to questions of fictional positioning.
But anyway, I don't agree that "this is not how D&D works". Here's Gygax, in his DMG (p 20), on the logical of the thief's ability to read languages:
This ability assumes that the longuage is, in fact, one which the thief has encountered sometime in the past. Ancient and strange languages (those you, as DM, have previously designated as such) are always totally unreadable.
In other words, if the fictional position of the thief PC is such that the language was one they might have encountered in their past (ie it is not ancient and strange such that it's not possible they might have seen it), then the player is entitled to the roll.
Gygax doesn't give advice on how to narrate failure, but "You've never seen this language before" might be reasonable. And of course AD&D already assumes that PCs are doing useful stuff in their downtime (DMG p 85; PHB p 106) and so the fact that the PC hasn't seen it before on
this occasion doesn't preclude them trying that language again in the future.
The original OA had more abilities of this sort, including the
contact ability, for the Yakuza class.
The real question, in many of these conjectured action declarations, is fictional positioning. If a PC is a first level character whose backstory suggests no link to the king, then what fictional position is going to support the action declaration "The king owes me a favour"? On the other hand, if the character is - at any level - in a tavern, then their fictional position clearly supports the presence of a nearby dude to punch. (Unless there is some other established feature of the fiction that suggests or dictates that the tavern is (near-)empty.)
Another issue, in some of these cases - and this is something I've discussed with
@hawkeyefan over the last few pages - is consequences for failure. What is the consequence for failure on the Diplomacy check to establish that the king will (for whatever reason that is appropriate given the PC's fictional position) grant a PC an audience? I think a lot of the more hostile discussion about resolving these sorts of action declarations tends to assume that there are no consequences for failure. But there is no reason why that should be so, in D&D any more than any other RPG.