Having the FDD trying to talk to you during a display is not going to help in the slightest and would inevitably lead to some very significant confusion. It makes sense that the FDD has the power to 'red card' you during any display - he may have seen something significant that the display pilot hasn't seen, but I can't see him having enough realtime data to hand to make a sensible call about stopping you at critical gate points.
You'll never get able to guarantee a display pilot won't crash. Once in many many hundreds of displays an accident will occur which will involve members of the public. It's the same with commercial aviation. Have a read into the provisional report on the Turkish Cargo 747 crash. An experienced crew managed to let the FCS fly them down to DH almost 2nm beyond where they should have been. A GA actioned about 4 sec after passing their 100ft DH meant a crash was inevitable. Just staggering that a crew could screw-up in style killing themselves and 35 innocent others on the ground. Thankfully these tragedies are invariable infrequent, but you'll never stop them happening.