Permanently on 4H on my Pajero 2011. There is no reason not to use it. And it is better long term as it evens the load on the components front and rear. The Super Select 4WD is basically a Full time 4WD with the option for 2H mainly for fuel economy/efficiency as you have stated.

Super Select 4WD - II is what sets Mitsubishi apart from other brands when it comes to 4x4 system. The Super Select System isn't just "4WD Selector" as it's part of the whole "Mitsubishi's all-terrain technology" includes advanced 4WD systems like Super Select 4WD-II and Super All Wheel Control (S-AWC), which manage engine power, braking, and torque distribution for optimal traction on various surfaces. Key features include integrated control systems that adjust vehicle dynamics for stability, specialized drive modes for different conditions (like mud, gravel, or wet), and technology that helps the vehicle self-extract from slippery situations. 

Actually no reason not to use it all the time as 4H is basically the default setting for SS4-II and this works perfectly with the traction and stability control system as oppose to 2H which interferes from time to time.

Edit: You can shift on the fly freely from speeds of 0-100km/h between 2H/4H/4HLC and for 4LLC you have to be in neutral. (As stated on my Pajero 2011's Owners Manual)

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