It comes down to attack surface minimization. The US system of selections is carefully engineered to facilitate a wide range of vectors of attack. These attack vectors are deeply entrenched and fortified. If an interloper attempts to prevent fraud and conduct an actual election, they will be overwhelmed by the agility of the enemy.
So, introducing voter id within the system reduces the threat surface, allowing the good guys to concentrate the efforts on the remaining dozens of threats.
"Voter ID" is a distraction in a few ways. All those countries who require voter ID are still compromised by election fraud.
It comes down to attack surface minimization. The US system of selections is carefully engineered to facilitate a wide range of vectors of attack. These attack vectors are deeply entrenched and fortified. If an interloper attempts to prevent fraud and conduct an actual election, they will be overwhelmed by the agility of the enemy.
So, introducing voter id within the system reduces the threat surface, allowing the good guys to concentrate the efforts on the remaining dozens of threats.