In any case, amendments to the Constitution would be necessary. They can in some countries where the executive branch is selected by the legislature. The separation of powers in our federal and state governments would prevent such problems. There are actually many multiparty legislatures in the world that are very stable. No, because people can and will choose representatives who live near them, live in a community with similar concerns, or can otherwise represent their local interests.
People use their power of choice to ensure that their local interests are represented.
This is vastly preferable to voting systems that force this choice upon people, regardless of their other political interests.