I have advocated something similar to this for years. Already large metropolitan states i.e. Calif. and NY give winner-take-all scenarios, even though if you look outside those metropolises the population often has different demographics.
It would have to be a two-part fix; CD representation and the outlawing of gerrymandering.
What is fairer than the overall popular vote winner getting the two Senate rep votes, but each HR district giving its single vote? It would also force presidential candidates to pay attention to all states and their issues.
However, gerrymandering needs to cease nationwide. State districts should be drawn as much like a checkerboard as possible, with consideration for natural barriers (mountains, rivers, bays).