The penalties are even higher for tax fraud and that doesn't stop the US Treasury losing tens of billions per year. It used to be hundreds of billions per year 3 years ago. We implemented extremely strict measures at work to reduce that number to reduce frivolous claims as well as to match the right person to the right claim.
As to voter fraud, there is an underreporting problem. If a poll worker is doing their job, they turn away people who are in the wrong place and send them to the right polling place. That doesn't get logged anywhere. For certain election contests in Ohio, those can be as small as impacting a single precinct in the case of liquor license approvals. In my county we've had tied elections as well as automatic recounts on state & local questions due to the margin being less than 0.1% and that was when we had butterfly ballots in our part of Ohio.
Normally elections problems here don't go to the point of prosecution. They're handled at the polling place and resolved there. People who aren't supposed to be voting in a certain precinct get routed to the right precinct after the local workers call and consult the board of elections to exhaustively search out the person's identity. Anybody violating a voter's rights here would get beat up by the other members of their precinct's panel before the board office even got involved, figuratively speaking.
A problem you raised as to the "exact match" and North Dakota addressing issues is that at least in Ohio we have several types of ballot questions tied to specific geographic territories. If you're in the specific territory you can vote on the question but if you're outside it you cannot. Certain precincts have to have up to 4 types of the same ballot due to different "special districts" like school districts not completely covering the precinct. One election I worked had three parts of the same precinct situated in three separate school districts with three separate school board races and it all depended upon your street address which district you were actually in. That precinct is still intact for now but it may get dissolved so we don't have that farce again.
Having to have an address and having to have ID to prove it is not a tremendous hardship in contemporary society. Without that ID, you cannot access any federal installations (i.e. free-standing Social Security office, a federal building, a federal courthouse, military base, etc.) shortly due to the REAL ID Act of 2005 shortly entering into full force. It'll be almost impossible to purchase alcohol or cigarettes without it. Banks and bank-like institutions will want to see it if you open up an account. Even a trip to the drug store or pharmacy can result in a need to present identification. You'll also be unable to board any aircraft to take a flight soon, too, if you lack ID. Having inconsistent ID causes havoc with all the preceding things, too. If possessing valid, unexpired, government-issued photo ID is a problem then perhaps a person has deeper matters to get in order first before doing anything else.