Mozart used the movement of a semitone downward a lot to end phrases. It's used a"sigh" of sadness rather than to establish confidence as in spoken English. I watched a few videos about it, and I have to say that in my ears, it sounds as if a downward inflection in English is actually just staying on the tone, because the default is to go upwards. When someone actually goes downwards, it easily sounds sad or condescending.
Depending on context there might be some connection between the two phenomenon, but anyway, I'd say that in music, the way to establish a solid point is achieved by playing the root note twice. The interval beforehand is less relevant, but perhaps downwards works better than upwards. That's my opinion anyway.
I hear what you're saying.