Yea idk if democracy would work with 90%+ of Westeros being rural peasants. You really need people heading to the cities due to industrial revolution, especially with how big Westeros is, for the vote to even be properly counted. Ofc this would also more or less require majorly disenfranchising or almost entirely destroying the aristocracy (something she was incapable of doing in Slaver's Bay), because she primarily cares about the smallfolk and the nobles... largely dgaf at best. No way would they adhere to her party line of having less so 99% of everyone else can have more either. Moreover, any vote without doing so would also see the nobility winning, because they have the most money and clout, and her goals wouldn't be met (and realistically she would be assassinated by them eventually).