I've said before that one factor in U.S. election complexity is the variety of requirements and practices in the balkanized election system. But people still (rightly!) ask, could the federal government do more to help? For a good perspective on that question, I'll point you to a New York Times editorial, Voting Rights Are Too Important to Leave to the States, by Adam Cohen. The short answer is that yes, the U.S. Constitution gives the federal government the right to regulate federal elections. The editorial gives some good examples of potentially useful regulations, and speculation on why its not forthcoming.
It also has a good explanation of the position that voter ID is a problem for election access. (If anyone knows of an equally good presentation of the typical "pro" case for voter ID, I'd like know.) But the broader picture of election access is just as important. When I recently wrote on technical risks of voter ID, I should have pointed out that the same idea applies to almost any new requirement or process around voting, because almost any case involves new technology. If somebody gets the tech wrong, then voting access is impaired. But as Adam Cohen points out, each state gets to make its own choices, and that multiplies by 50 the chances that some choices have negative side effects. Then, when you factor in computing as part of each state's implementation (of voter registration, voter ID, ballot design, or anything else), you might be getting scarily good odds that a computer error results in a barrier between a voter and their ballot, or the ballot being counted.
Last thought: what can we do to help? Do our tech work, create de facto standards on election automation, and give the Federal government more things to standardize on. In the long run, it might end up reducing complexity of elections, and increasing trust.