Why was bronze chosen as a third place signifier?

The ranking Gold > Silver > Bronze > Iron (> Lead) dates from Hesiod: see Ages of Man. Bronze for toolmaking in common use is older than Iron; Hesiod was aware of that, which is why his Bronze Age is earlier than his Iron Age. Gold and Silver would have outranked Bronze and Iron, because they were precious metals (better suited to describe an ideal past), and Bronze and Iron weren’t.

Per Wikipedia: Bronze, the ranking in Olympic medals derives from Hesiod’s ranking, but was only put in place in the 1904 Olympics; before that, it was 1st place Silver, 2nd place Bronze.