Why is a picture ID opposed for voting?

In rec.aviation.piloting Orval Fairbairn wrote:

If, as you claim, they are crooks, what is to stop them from
substituting your ballot for one that is already marked? How do you know
that YOUR ballot didn't just go into the shredder?

When you come out of the voting both you hand you ballot to a worker who
tears off a tag, hands you the tag, and puts your ballot into a locked
box in front of you and there are no shredders or copiers in the room.

In addition, there are monitors in the room to ensure everyone is doing
what they are supposed to be doing.

This scenario is just as unrealistic as being able to copy voter information
in the polling place.