> Most issues that voters care about are not local issues, so why do need a system to carve up representation along geographical boundaries?

That seems more like ratifying a failure mode rather than fixing it. Having geographic representatives mean that area is less likely to get railroaded in various ways, because they have an advocate who's accountable specifically to them, rather than some diffuse ideological block.

Also, a lot of issues that voters care about are actually local issues made national through centralization.