Liquid democracy inherently prevents the kind of unequal representation we’ve seen under redistricting. In a district-based system where 50%+1 wins, there are always some votes going to waste, either extra votes for someone who already won or votes for the candidate who lost. Gerrymandering is effectively picking whose votes get wasted to ensure the outcome you want.
In liquid democracy, the person you chooses never loses and your vote always matters. If a proxy gets more votes, that just means that that proxy has earned more influence.
Harder to fix are the Senate and Electoral College. Eventually, liquid democracy would likely result in amendments to the Constitution to address these issues. Short of that, the Senate can only be fixed by electing Senators who commit to voting based on the outcome of a national liquid process. This would mean those Senators would sometimes vote against the will of their state voters to represent national ones, a difficult promise to sell. Similarly, the electoral college can only be fixed by changing how states allocate their electoral votes.
Both of these fixes are similar to non-liquid solutions to these problems, but would be far easier to implement if it involved convincing voters rather than politicians with a conflict-of-interest.