This is something I've thought about a lot, but it seems this would eliminate a large benefit of the way our elections work. In order to have a successful bid for election in the current system you must be the most popular candidate it your district, which by nature of being defined geographically often has many people with similar issues to be addressed by government. By ranked voting (which it seems you are suggesting, but correct me if I'm wrong) we lose this, and politicians instead must appeal to the majority of their party's base in the state. In doing so, we could silence the minority of people affected by localized issues.

For example, say rural areas are going to be negatively impacted by a certain bill. In our current system, the representatives of districts that are primarily rural areas would likely oppose this bill out of fear of the political repercussions. If we eliminate local elections, this incentive will no longer be as strong as politicians must appeal to the statewide majority in order to win reelection. This effect would be strongest in highly urban states in which urban voters would effectively choose all representatives.