ISecond, this might actually increase interest in statewide elections, which are mostly ignored nowadays. How many people here can honestly say that they know much about their state legislators? All the vast majority of people care about today are federal elections.
Alternatively it would convert the legislative elections into contests over which person would be elected Senator. People would watch the senatorial debate (ala Lincoln-Douglas) and decide who to vote for in the statehouse race, totally ignoring all local issues.