I'm approaching the questions in the title from the perspective of a hobbyist, certainly not a pro where what is played is what the job demands.
I have noticed, since beginning my comeback twenty-one months ago, that some of my instruments fit better and are simply more comfortable to play than others. All of my Bb trumpets provide more playing comfort than the cornets or flugelhorn, and a couple of the trumpets distinguish themselves.
The trumpets that fit best have the most favorable weight distribution for me while being played and serve to position my arms most comfortably. Does this matter? I suggest it does. Good playing mechanics are more easily maintained with a good fitting instrument, in my humble opinion.