The Asset is too important, and too high risk, to be involved in trash parties. STRIKE, on the other hand, are disposable and expendable. It doesn't matter if they die (hey they have dangerous jobs, death is always a possibility) and those that survive get The Chair and falsified medical records.

And who better to brutalise these men and women for the amusement of the higher-ups than the Soldier? He has no choice but to follow the orders given to him, regardless of how extreme they are, and he carries them out perfectly.