As I said, it's not outside the realm of possibility. There are some historical parallels, but it strikes me as fantastical to see a hereditary monarchy transition straight into democracy.
I think it's overly dismissive to say there are 'some parallels.' There were collectively thousands of years of history of non-monarchal governments most of which sprang from monarchies (all of which? I'd have to double check).
Also, I rewatched the scene to make sure I wasn't insane here: Sam suggests leaving it to 'everyone' and gets laughed at.
Bran, the child of one of the great lords, is set up as king by a council of a dozen of the highest-titled people in the country. And it's set down that the new king will always be chosen "on this spot" by the 'lords and ladies of Westeros' -- i.e. the highborn. And those highborn lords, for the record, are still hereditary titles and are not elected positions.
I.E. non-elected nobility gets to elect a king from their number. It is 100% not a democracy. It's functionally the exact government that dozens of places in medieval Europe actually did have.
Most fantasy cultures are lifting from Charlemagne's Frankish period, methinks. Going from that sort of culture directly to a democracy without any explanation for where these people *soaked* in monarchy to the point they literally believe in the divine right of kings is indeed unrealistic.
None of that's true, though.
Charlemagne's Carolingian Empire was late 700s to early 800s and would probably be unrecognizable as a 'medieval kingdom' to most fantasy fans. Speaking specifically about GOT; Westeros is 100% based on the War of the Roses period of English history. A totally different country, a very different style of government and culture, and about 700 years later.
In either case, both cultures existed side-by-side with non-monarchal governments. The 'divine right of kings' was an excuse, not a truism that everyone bought into. Trump can do the same thing - call himself a King and say he's ALLOWED to do all the things he's doing because of his position. Doesn't mean all of us peasants just agree that's true and can't possibly fathom another way.
And again, this wasn't even a peasant uprising into a fledgling democracy. This was a cabal of powerful lords deciding that THEY should get to choose who is king. There's LOADS of precedent for that. Hell, they tried it in England with King John and made a terrible Robin Hood movie all about it.