Every culture that went through the stargate was steeped in SG mission reports which described their destination, and most first-contacts were made by SGC personnel. To these worlds, SG members are a bit like a blend of the early explorers of North America, the Pilgrims, and the Founding Fathers, giving them a gravitas that future squabbling politicians can never match. Almost all of the planets, whatever their differences with each other or the current core worlds, will meet and hear out what an original SG member has to say. This makes the SG team members natural diplomats and troubleshooters. If not George Washington, they are certainly Miles Standish, Daniel Boone, Lewis and Clark, and Davy Crockett.
If Daniel Boone or George Washington popped out of a gate tomorrow I doubt they would take on any kind of active role in our life. They would be of huge historical interest but that would be about it.. and I think the SGC team would be in the same boat. Just because everybody respected Scotty didn't mean he was put in charge of anything.
I would LOVE to see Stargate set in future earth. It certainly takes more planning and plot than random medieval villages which are all the same story.