I can't put an advantage to the system either, but that is what is fitted to the tractor I have. It's the symptom of running on after the ignition switch is turned to off that leads me to say the fuel valve is open when the solenoid is de-energized. It could be some other control or input. I've read the service manual, and thoroughly investigated the operation of the Control Unit. It's a "Black Box" to me. Three wires in. One is fused 10A directly from the 12v DC bus, two come from the ignition switch. Two wires out to the solenoid, and a ground.
The problem could be as simple as a loose fuse holder on one of several circuits.
ETA These tractors were offered by the SDF group with an air cooled diesel engine as an option. Looking at the wiring schematics for that version, the fuel cut off solenoid is wired "logically". That is, a single wire from the key switch. Although it is a bit confusing in that the single glow heater is in series with the solenoid winding. Figure that one ! ;-)
OK Here is why the system is the way it is.
Woodward | External Solenoid Control Electronics
It takes a lot of force to actuate the fuel valve. That goes along with how solenoids function. Force and distance etc.