What will you do even if they give it to another SF? None of the routes in the south have an MPS higher than 110kmph (except BZA-BPQ route). So, even if you give it to an SF, it doesn't make any difference.
And this is the biggest misconception. LHB coaches are not given for speed. They are given because they are a new design compared to the 65 year old ICF coach design. LHB coaches will be given to every train irrespective of what type of train it is. There is no order of priority or preference.