You can make shadow softer by moving blocking object farther from the subject. Of course you would also have to make it bigger so that its shadow remains at constant size. Changing sun's size is a cheat, so it's better to avoid that if possible.
Can't say much about volume fog though, since i barely ever use it.
Thanks for your suggestion, I usually try all this stuff to achieve the desired result but still hard to get what I want. You know my purpose is concept art so I have to manipulate everything I can to see what I had in my mind, this way I have to increase the sun size, maybe if it was possible to do all this with only HDRI and no sun it would be better but in one hand it's hard to find a good HDRI map among 1000's of confusing ones and also the scene loses light directionality without having a direct light source. About volume fog I am using a big box here with a corona volume light applied, that's what we usually do in blender.
It can be done quite closely to what can be achieved w "Physical Sky & Atmosphere"... but first would be nice to see what your current result looks like.
Here's a quick test w/ latest daily.

Edit:
Added "Volume effect"

Thanks for your effort Burnin, I really appreciate your time and attention to this issue by making a test scene, I am happy you're familiar with PSA addon, honestly I wanted to make this scene in blender but I am really tired of Cycles as I cannot get those deep light and shadows of corona with it..
Your result is really good, I guess one problem here in my scene is that the sun itself also exists in camera view making it hard to hide undesired issues like blocking geometries (either plane or cube) with the ground. Another problem is that I still get sharp shadows in contact areas between the building and the ground, and that's interesting it's not happening in your scene. Anyways as you mentioned I have attached the scene and its screenshot to see your opinions.