Quote from kbrockman:
"Has there ever been an accident where the non-moving throttles were a substantial contributing factor, honest question, I don't recall one but there might be those that do ?"
If there has, it's very hard to establish beyond doubt.
During final approach using A/THR on an aeroplane with "driven" thrust levers, it's normal good practice for the PF to rest his/her hand gently on the levers. That applies whether the AP is being used or not. As has been said, it has the twin advantage of providing tactile feedback to the PF, and enabling him/her to override or modify the A/THR inputs on the rare occasions that may be necessary.
It's also been pointed out (particularly by Airbus Industrie) that, in a decaying-speed situation, any forward movement of the thrust levers MIGHT be taken by the PF as sufficient indication that total thrust is increasing. The only true indication of that are, of course, the N1 and/or EPR gauges. However, what can be said is that an absence of thrust-lever movement would alert the PF to A/THR failure. On FBW Airbuses, the thrust levers are stationary in the CLB gate until landing, unless the PF is using manual thrust.
In the early days on the A320, there were a number of incidents on visual approaches using A/THR during which the PF did not realise that, due to his mismanagement of the FMGC and with one or both FDs still on, the system was still in IDLE mode (OPDES). In those days, there was no protection in IDLE/OPDES mode to stop the speed dropping below VLS (until Alpha-Floor). This was a contributory factor to the fatal accident of an Indian Airlines A320 at Bangalore.