I do notice how the side that is pro-increased agency has a bunch of actual play examples showing it to work, but the side that's against only has weird hypotheticals about eggs in lifeless vacuums and dimension hopping to modern day America
First, if you're trying to have an actual conversation with people (as opposed to score random points on the internet that cannot be turned into prizes), it's usually best to avoid labeling your side with terms like, "pro-increased agency."
Second, it's best to avoid turning everything into two sides, if you actually want to have a conversation.
Third, the purpose of "weird hypotheticals" comes from a Socratic method; here, to show that an absolute statement (this power must always work, even if it is just a ... background feature, which is not supposed to be a major ability) is not correct. That's it.
That said, there are, quite literally, an infinite number of scenarios where the fiction (in most assumed D&D games) would not allow the "Position of Privilege" feature to work. Here's an easy one-
The party is engaged in combat with a group of Orcs. On the third round of combat, the character with the Noble background (we will call him Chad) says, "I use my Position of Privilege to tell the orcs we are fighting with that they must cease fighting and give me an audience with their chief."
No?
The party is engaged in combat with Mind Flayers. In the middle of combat, Chad says, "I use my Position of Privilege to tell the Illithid to recognize my nobility and take us to the elder brain."
No?
The party is about to fight the BBEG, a local warlord. But the local warlord laughs and sends a group of his henchmen to kill the PCs, with the explicit instruction that they KILL THEM. But late in the combat, with the tide turned against them, Chad says ... "Hey, I tell these henchman that I'm a noble and stuff. Time to get an audience with the BBEG!"
Yeah. These seem silly ... because in most games we assume players to operate in good faith, and we wouldn't
expect them to use this background feature in that way. Just the same as we wouldn't expect the DM to "just say no" to a reasonable use of the feature! But this is the entire point of this conversation. People are just talking past each other.
These are different playing styles, with different built-in assumptions. These things don't normally arise at the vast majority of tables, because the vast majority of tables consist of people who talk to each other and are trying to have fun, not people arguing with each other in order to assert that their playing style is superior with the use of hypotheticals.