You could print a receipt that contains the voter's selection. The voter would then verify the selection and deposit the receipt into a receptacle. The voting machine results could then by audited by comparing the receipts to the voting machine's history.
I should clarify my question "why" is specifically about conflating votes with timestamps. I have more general concerns about voting machines, but those have been raised elsewhere in the comments many times by other commenters.
The timestamp of each vote in the machine could be useful during the audit. Imagine you found a discrepancy, you'd then want to determine when the discrepancy started.
If you're able to determine some subset of voters from the attached timestamp information, then you're equally able to use that data to harass people who didn't vote for the candidate you want.
