Voter registration cards are on the identification document list in that link, they don't have pictures on them.
Either way the requirements to vote are currently less strict in many places than the requirements to get a photo ID that can then meet the requirements of voter ID laws.
That, all by itself, means it will affect some percentage of the voters in an area, and that means it can easily affect the outcome of an election, at the very least for a period of time that may span multiple election cycles.
And that is the real reason voter ID laws are constantly being proposed.
Constantly re-arguing the theoretical neutrality and easy availability of ID (which is generally neither free or easily available, in some cases deliberately) ignores the practical effect of voter ID laws, and the motivations of those pushing for voter ID laws.