Until Bran shows up, the Three-Eyed Raven is a mythical figure to everyone aside from maybe the Wildlings. Having him show up in the flesh would be a bit like your long-lost uncle trying to convince you he's been away training to be the next Santa Claus, à la Tim Allen. You would have questions about what exactly his existence means for humanity and also, you know, what his actual powers were. Old Nan probably mentions the Three-Eyed Raven in her bedtime stories to the Stark kids, but on the whole, there aren't many people in the Seven Kingdoms who think those stories are about an actual person.
That's why it's extra weird to see people like Sansa just accept Bran's claim at face value based on him describing her very traumatic wedding night. Sorry, little bro, you making things awkward isn't going to distract me from asking what the heck an actual Three-Eyed Raven does, how you got the job, or what it means in practice. Like, most importantly, what do you do? Why does humanity need a single person to serve as its collective memory when we have historians and folklore? I know things are pretty dire, but these are fairly basic questions that I expect people to ask a mythical figure who appears in front of them in real life.