But you're agreeing with me.
I think Bran gets elected. I'm more doubtful of the succession system implemented after that.
I think the implication there is that eventually Westeros does eventually adopt democracy in choosing government/rulers (Sam saying that wasn't just a random thing dropped into the script).
So basically what you're seeing the beginning of the end of the monarch/noble age of Westeros and the dawn of a new era.
Just like in LOTR, the ending is not just "Sauron dead, good guys win", there's an implied longer term ending that actually the "world" of Middle Earth becomes eventually Europe and the hobbits become the British (I guess? lol).
In both cases the elements of "fantasy" (like giants, trolls, white walkers, dragons, etc.) will eventually also be lost to time and become folklore.