Thermal control is critical during the scarification process. The Lid helps to maintain the temperature during this process.
However, when you sparge at temps of 168F typically, the temperature is not critical to the scarification since it has already been completed.
The temp of 168F is really to help "thin" the viscosity of the wort and to neutralize any continuing enzyme activity.
The Important Aspect of Fly Sparging is to maintain just enough water on top of the "set" grain bed to hydraulically push the wort through the grain matrix.
There's really no one reasonable way for the home brewer to do this -that's to visually see the Mash.
The design follows the rules above:
1 - Temperature is Critical during the Scarification Process.
2 - Water Management is Critical during the Sparge Process.
Hope that helps answer your questions on why we designed our Tun in the way we did.