To add onto what other people are saying:
When a blade breaks, not only is there a potentially sharp point on the new end of the blade, but the blade that's left attached to the handle is probably more stiff - possibly quite a bit more stiff - than the original sword. This is for a couple of reasons:
1. Leverage: short things are stiff, long things are floppy.
2. Profile: I honestly have no idea if this applies to olympic swords, but in historical swords used for combat, blades will often be quite wide at the base and taper towards the point.