I misread your previous post. Now looking back at it, you were talking about the traction control system. I apologize. (I have always been told that engineers can't read, and attorney's don't understand common English, and I guess I just proved this.
)
You are correct, the ETC will have a slight lag due to the wheelspin having to be detected, then running the solenoids and valves to apply braking action to the spinning wheel. Lag is probably about one-to-two seconds, but still a lag.
The Eaton E-locker is what I described and once it is locked, it is locked until you unlock it or exceed 20 mph, at which time the controller unlocks to prevent any damage. The E-locker is almost instananeous.
H3 Hummer:
In the photo you show, the H3 will pull out without an E-locker. I know, I did this exact same thing in TN over labor day, and it pulled out slow, but it did pull out (I was in 4-low). I then put the H3 in the same position, and engaged the E-locker, and it pulled out a lot easier.
The traction control will stop the right rear wheel from spinning and the front tires will pull. I have been in similar circumstances with one of my jeeps without an e-locker and in that case, the front wheels pulled me out.
If you have a front and a rear in the air, that is where the E-locker excels.
I will now go and finish my bloody mary.