its considered a soil-less mixture because no dirt or soil is involved.

So, if soil is so important for its minerals, is Mel's Mix really as ideal as he (and many followers) claim? Or is there some reason that the principles about soil/minerals being important don't apply to this mix?

The minerals and nutrients are derived from the rich compost that make up 1/3 of the mix. That's why it is so important to use good compost. I actually supplement with compost tea as well.