Basically, my opinion is that 3DS FE stories don't do the leg-work previous FEs did and it was in that leg-work that FE had potential to be something more than trite, cliche war stories and character romps.
I think the approach to character personality (and art) design has also changed and it exacerbates this, but I don't think it is central to the "problem."
For an example:
Just look at the child-producing mechanics of modern FE compared to those of FE4. In the latter, you have this grand tragedy and revenge of the righteous cycle, which contextualizes the child-producing system.
In FEA and FEF...you have skin-flint narrative rationales, and the main point is to service the expanded mating simulation. They don't even try in Fates in this regard.