This is true, but we must not take too much comfort from this.
When an accident does happen, it often appears to be due to a lack of old time skills, or even more bizarrely, modern techniques and BS paperwork getting in the way of such skill.
hec7or's comment says it all really.
I'm afraid that after engine start, I'm often filling out company paperwork or trying to update FMCs or deal with cabin crap while taxying due to the pressure we're all under these days to keep it rolling on short turnrounds.