> I believe just the starting of the timing is done by hand. The stopping is done when a contact is automatically detected.

That's exactly the issue, though - there are a handful of mechanisms in place to ensure that the clock stops and points are awarded properly - electrical equipment is used, buttons on the tips of the Epees are tested with a 750g weight, fencers test on eachother's masks before each match, testing kits are used to check wiring, etc., and the judges are there to watch movements to account for possible disputes. The task of starting the clock has been significantly overlooked compared to the task of stopping it.

Aside from this, the rules and the scheduling of matches are done with the assumption that there will be no major disputes, which needlessly compounds the damage from any dispute that happens.