Ya gots to read the article carefully, 'cause they're trying hard to fool ya.
The citizenship requirement is in place for registration, not for voting. If you're already a registered voter, you have no problem.
If they are turning away properly registered voters, then we have a real problem with the poll workers.
In my ideal world, all voter registration polls in the US would be purged on December 31, 2005. Then, all eligible voters would need to reregister prior to March 1, 2006. That should get it done in time for most election cycles. Then, I'd do it again every 10 years as a form of mid-cycle census.
Should reduce the fraud considerably, I'd think.
Law requires that the least onerous means be employed on citizens to impose such a re-registration demand as the means to prevent voter fraud. Your suggested ''ideal world'' would be far from such a least burdensome method.