> The entire idea of a geographical area selecting just one person to represent their views in a legislature is outdated and undemocratic.
I don't think that alone makes it undemocratic. Many systems implementing proportional representation elect a single person per geographic area but also create an overall balance based on the proportional vote. See https://en.m.wikipedia.org/wiki/Leveling_seat for instance.
It tends to a two party system which inherently can't represent people's views accurately. In the US you see people talk about white and black districts as if all white people think the same.
A proportional system means everyone's views are represented in the legislature and at that point compromises can be brokered.