Interruptions and chatter on the flight deck during set up is also a threat and ground staff/ cabin members need to be disciplined in this area.
Here you have the root cause: The last 5 minutes before STD/push back are the most stressed phase of flying, and the load figures often come at the last minute.
In most of "my" airlines I have seen how the stress makes the guys load-shed during the calculations. Why? Because there isn't enough time if you want to leave "on time", and OTP is the big mantra in most airlines.
In one airline we came up with a smart system: If you entered a GW less than MZFW it would block and give a warning. One day the crew attempted to enter the ZFW iso TOW, and when the warning came up they simply did an override. Result: Very close to disaster and a big hole in the tail. This is what pre-departure stress can do to you.
The OBAWS (Onboard Balance & Weight System) has been around for ages and is an excellent x-check reference, but the "Safety-is-our-main-concern" managements are very reluctant to pay the several thousand dollars for a system that does not bring revenue and whose sole purpose is to catch mstakes made by the excessively high paid pilots.
The last line of defence is the Speed Trend Vector found in most modern aircraft. If you don't accelerate 4KTS/sec you are unlikely to become airborne in 3000m, so you either go TOGA or abort.
During SIM trials in a widebody quad I gave the crews wrong figures which only gave them 60% of the required acceleration: They all overran the runway....In the 2nd attempts (and after a briefing) they all survived when going TOGA when they identified the slow acceleration (around 80-100 kts) - and they did not scrape the tail (but some close calls).
PS: The frog discussion is rubbish. I have checked several AF crews and they perform better than the average, but as with most of the old legacy carriers complacency is hard to eradicate. Not a unique AF issue.