De-aligning the visions and incentives of the many states is not a particularly desirable end-goal. For a sample of the result, one only needs to look at the European Union. For all its faults, legislation in the US is not approved or denied on the basis of whether it will let some states "get ahead" and so on. When a state gets nailed by an earthquake or a hurricane we provide military assistance and financial relief and get on with it.
The EU does not act in this fashion because they have strong sovereign states who act in their own interest, and are much the worse for it. When an EU member state gets something like a refugee crisis all the other member states just tell them it's their problem and they need to deal with it. They view monetary policy in the light of which member states it will benefit and which it will harm. They can't even raise an effective Federal military force.
Frankly this type of government already failed as the Articles of Confederation and the Federal system was drafted as a response, but that still doesn't stop some people from clamoring for its return. The Federal system already contains numerous sops to the interests of states, and should not be weakened further.
The House of Representatives already does a pretty good job of representing geographic areas. That's somewhat contrarian since people think of the Senate as the one that's supposed to represent geographic areas (states), but in modern times the House represents the geographic areas (large sparsely-populated areas with conservative membership) and the Senate represents the actual popular vote (nationwide, moderately liberal by a small margin but highly concentrated in urban areas). This is amplified somewhat by gerrymandering, but the truth is that congressional districts are inherently geographic areas and that's the feature the representation conforms to.
If you wanted the House of Representatives to be restored to its original vision, you would need to do exactly what the topic suggests and massively increase the number of representatives to drive the error caused by districting down to a reasonable level. That would be very different from any other large-scale government and would be ruled by informal power structures inside the parties, at which point you might as well just go to a parliamentary system.
While we're on the topic, if I could change one simple feature of US politics it would be for Senators to serve 4 year terms, with every state electing one senator every 2 years. The current system of 6-year terms sucks because parties very predictably dominate presidential elections and off-year elections, and you end up with Senators who are thrown out based only on the fact that they now face an opposite electoral climate from the one they were elected in, that will inevitably reverse on the next 6-year term cycle. There is a huge amount of "churn" here that in my opinion serves no purpose.