I was a little confused by your question, so I had to reread a few times.
Correct me if I’m wrong, but I think what you are asking is why the low doesn’t develop right under the strongest winds of a jet stream. You’d be correct in your observation that it usually develops downstream of a trough where upper level winds diverge, air lifts, and surface pressure decreases.
When the vorticity “stretches”, we get an elongated region of positive vorticity advection as opposed to concentrated into a tight vort max over one area. That spreads upper level forcing for lifting over a large area, thereby “diluting” the tendency for a surface low to form.
So it’s not so much the sfc low doesn’t “prefer” to be away from the strongest winds, but more like it tends to deepen where that elongated band of vorticity overlaps the divergence (left exit/right entrance regions) and the baroclinic gradient. While vorticity alone isn’t enough to develop a storm, that combined with upper level support will do it - there needs to be both.
The displacement you’re noticing is really a reflection of where the total forcing (vorticity and upper level divergence) both line up, which often ends up a bit downstream and to the left of the jet streak, not directly under the strongest winds.
Now when the jet core “rounds the base” of the trough, you’re right that we’re often getting into the mature phase of the storm. By that point, the upper level trough and the surface low have gotten more vertically stacked, and the low begins to occlude and weaken.
Sorry if this got too technical, but your question covers several different meteorological concepts, and the evolution of a cyclone where conditions differ between the early stages of development and when it matures.