How does that prove that you only voted once? If I know someone's name and address (and by extension their electorate) I can rock up and vote as as many as I want.
(A few people voting more than once is unlikely to change the results of an election. If enough fraud is detected to impact the results, they'll run a new election.)
Given they are usually random primary schools and churches... do they have cameras?
I think the bigger deterrent is just the risk of claiming to be someone who already got ticked off at the same booth, which would immediately raise suspicions.