It’s about more than the failure.
Yeah, they allow player agency!
Welcome to the conversation!
How is critical. It’s not the failure itself, it’s how that was determined for the player. How did the player (not the character) fail?
If they failed because they tested the odds and it didn’t work out… they made a roll and didn’t meet the target… then that is them making an informed decision and it not working out. That’s agency. The ability to succeed or fail is up to them.
If they fail because the DM says “no”, then it’s not really up to the player, is it? So there’s no agency there.
I think it’s a matter of it being so off base that it’s hard to believe someone would make it in good faith. Honestly, your idea of agency is way off.
This would apply if the entire game consisted of the noble declaring audiences all the time and nothing else.
It’s such a specific thing that will come up only occasionally. The idea that it’s game breaking for the DM to yield this tiny bit of authority is bonkers.
Tell that to Aragorn! Or Arthur! Or Odysseus! Or dozens of other examples from myth and legend that clearly served as inspiration for the feature!
And yet in Game of Thrones, the characters get audiences all the time, with all manner of other nobles, from friends to enemies to strangers.