It’s hard for me to imagine that the actual outcome of such a proportional representative system would be worse (in my judgment) than the current US federal district system, but the theoretical criticisms are obvious. For instance, it makes sense to have representatives represent a specific area who were supported by a majority of voters from that area. That way, the representative can in theory represent specific interests that are disproportionately important to citizens from that specific area (e.g. agricultural issues for rural areas or public transportation issues for urban areas).

Of course, drawing these districts (in either system) is an inherently arbitrary process which can lead to counterintuive or obviously unideal results, the most obvious example of which being gerrymandering. But at the end of the day, unless we have a one world democracy, borders must be drawn. National borders are “easy” in the sense that they tend to be formed not by a democratic political process but rather historical conflict.