Should have replied to this earlier, but this is not strictly true. Depends on what the weak element is. If you’re talking about the roadbed, and assuming no flaws in building, then you are correct: the part under the most stress will be the center of the simply supported bridge.
However, it could be the problem is in the footings or anchors, in which case the bridge would fail at the supports. Or it could be a suspension bridge, and the cables break.