One would think that the whole reason for registering with a bunch of different addresses is to vote at as many addresses as possible, which means casting multiple votes. Otherwise, why bother?
Obviously, multiple voting by the same individual is a common mode of 'Rat cheating. I think you probably heard, for example, of Dem voters admitting in the last few presidential elections that they were registered and voted in more than one state.
Then you have instances of buses driving the same voters around to multiple polling places. That kind of cheating happens to be aided and abetted by early voting laws in states where it exists. I know it may be unpopular to say this, but abolishing the Clinton-era "innovation" of early voting wherever it exists will serve to improve the integrity of the election process.
She didn't register at a bunch of different addresses. She registered at only one -- it just wasn't an address she actually lived at. She did that so she could run for office in a district she didn't actually live in. There's zero indication that she had any interest in voting more than once.
I actually disagree with you. In my experience with elections, it's high volumes of voters on election day that cause chaos and allow for fraudulent voting. Election officials get overwhelmed and can't cope with the numbers, so they let people slide. Early voting reduces the flow to a more manageable level and helps officials do due diligence if there's any suggestion that person might be registered more than once.