Why is DNA polymerase added at the end of PCR reaction?
True, the template is double stranded, but the primers could begin amplifying themselves, and any other stray DNA. You don't want any nonspecific amplification in the early stages that could compete with the target fragment. Also, even though Taq polymerase is a very hardy enzyme, it is standard practice to treat enzymes with special care, on ice so they don't degrade (although I have forgotten them on the bench overnight, and they survived that).